Estimating and evaluating proxies for the marginal tax rate.

Abstract:

Graham (1996b) tested proxies for the marginal tax rate and derived a number of important results. This paper re-examines two factors raised by Graham's work: the impact of tax regulations on proxy performance, and the presence of bias in proxy construction. Simulation methods create a simple tax world where the `true' marginal tax rate is known. Tax proxies are ranked against this rate using regression diagnostics. Manzon's proxy is the best performing of the simple tax proxies tested and is an unbiased estimate of the underlying tax process. The impact on proxies of tax loss treatments is assessed. Evidence is found that proxies differ in performance across different loss treatments. Evidence is found of an inbuilt preference between some variants of a simulated tax proxy and the tax benchmark.

Keywords:

TAX RATES; TALOSS TREATMENTS; SIMULATION MODEL.

1. Introduction

The impact of tax effects on firm financial decision making has been a central research question since Modigliani's and Miller seminal papers of 1958 and 1963. Since then the focus of tax studies has broadened from capital structure research to include a wide range of corporate decisions, for example, dividends (Poterba & Summers 1984), asset allocation (Dammon & Senbet 1988), mergers and acquisitions (Hayn 1989), multinational corporations (Scholes & Wolfson 1992), pension choices (Clinch & Shibano 1996) and capital structure decisions (Graham 1996a). These and many other empirical tax studies use a variety of tax proxies and a range of data, but have often met with limited success. In particular, the tax effects expected do not always find support in the data examined. One possible explanation for this lack of success is the choice of tax proxy used. The objective of this paper is to investigate the comparative ability of various tax proxies to capture an underlying `true' marginal tax rate.

Similar questions on measuring tax effects have been addressed recently by Shevlin (1990, 1999) and Graham (1996a, b) who assessed a number of marginal tax rate proxies used in prior research. The rationale for their studies is that despite the acknowledged importance of the marginal tax rate in corporate finance research, commonly used proxies rarely reflect the intertemporal and legislative characteristics of taxation. Intertemporal effects can occur when firms have taxable income components, such as losses, that shift tax obligations into a time period other than the present. Legislative effects arise from specifics of the tax code facing firms with regard to statutory rates, rebates or exemptions, etc.

Shevlin (1990) examined marginal tax rate estimation and illustrated the impact of different tax proxies on the measurement of the marginal tax rate of a firm. He demonstrates that net operating loss (NOL) rules can have a significant effect on the values of the marginal tax rate and shows that a simulated tax proxy constructed from firm data performs better than simpler proxies as measures of expected marginal tax rate. Shevlin (1999) adds support to his earlier findings that measurement and evaluation of NOL treatment affected the quality of the marginal

tax rate proxy and hence on its performance as a indicator of tax performance.

Graham (1996a) builds on Shevlin's 1990 paper and captures a strong tax effect using a simulated tax proxy based on the mean and standard deviation of change in observed taxable income for a firm. Graham calls this proxy the `forward sample' marginal tax rate (MTR). He further demonstrated (1996b) that this simulated proxy of the marginal tax rate (MTR) is superior to other commonly used proxies against his chosen benchmark. The chosen benchmark measures an estimate of marginal tax rate for any given year calculated on the basis of the known values of revealed taxable income for all years relevant to the calculation of tax loss effects. Graham calls this the `perfect foresight' benchmark since he `peeks' into future actual realised taxable income values to calculate the marginal tax rate.

Graham (1996b) noted that this type of tax benchmark measure is potentially problematic since the benchmark, itself, is an estimate of the unknown `true' marginal tax rate. In other words the benchmark used to assess other tax proxies is itself a noisy proxy for `truth'. This raises two questions. First, the presence of noise in the benchmark tax rate potentially understates the performance of all tax rate proxies investigated. Second, the use of common `perfect foresight' information to estimate both the mean expected taxable income used in calculating the simulated tax proxy and future taxable income numbers used in the benchmark tax rate could result in correlated noise between the two measures. This potentially biases the investigation in favor of the simulated proxy.

To investigate these issues further a simple economic setting is simulated where the `true' expected marginal tax rate can be identified to investigate the performance of various tax proxies.

Although the simulated economic setting is simple, it reflects characteristics assumed in prior research when estimating marginal rates. It therefore provides a convenient setting within which to study tax rate proxies.

The results indicate that correlation in noise between the benchmark tax rate and simulated tax proxy does induce a bias favoring the simulated proxy over alternative proxies studied. Nevertheless, after removing this bias, and consistent with Graham's (1996b) conclusions, the simulated marginal tax rate proxy generally best captures the true marginal tax rate. Also, the simulated tax proxy performs particularly well for subsets of firms with either a short history of taxable incomes, or volatile income streams.

However, under certain circumstances, such as low volatility in the underlying taxable income stream a simpler proxy such as Manzon's proxy can perform quite well. In fact Manzon's proxy outperforms the simpler proxies and is unbiased in its estimate of the underlying tax rate series. This choice between a simple proxy and the simulated proxy is then based on a cost benefit trade off between the incremental improvement in estimation and the reliable computation of a more complex tax proxy.

Modifications to the tax regime reveal that when no tax loss carrybacks exist the performance of the statutory rate is superior to that under a tax regime allowing carrybacks.

The remainder of the paper is structured as follows: section 2 describes the simulation model and assumptions; section 3 sets out the testing methodology; section 4 presents and discusses the results; and section 5 offers some conclusions.

2. Model and Assumptions

The simulation is designed to construct series of marginal tax rates for a variety of `firms' over an extended time period (forty data points, or `years'). Firms are identified by the moments of change in taxable income. The mean ([mu]) is constant for all firms, however standard deviation ([sigma]) varies in relation to [mu] from small through large. The base model for constructing taxable income assumes that change in taxable income follows a random walk with drift.

giving [DELTA]T[I.sub.it] = [[mu].sub.i] + [[epsilon].sub.it]

T[I.sub.it]= T[I.sub.it-1] + [DELTA]T[I.sub.it]

where: TI = taxable income;

[DELTA]TI = change in taxable income;

[mu] = the mean of change in taxable income for firm i; and

[epsilon] = distributed N~(0,[[sigma].sup.2]) where [[sigma].sup.2] is the variance of the change in taxable income for firm i. Both [mu] and [[sigma].sup.2] are exogenous and therefore known. The choice of a random walk allows a tax series in the style of Shevlin (1990) and Graham (1996b) to be constructed. The marginal tax rates are modelled on the basis of a taxable income stream, a discount rate, tax rate and tax regulations.

To compile a simulated data series for each firm several steps were taken. A series representing forty years of taxable income is created starting with time zero whose taxable income value is zero dollars. Year one is year zero plus change in taxable income, as above. This mean and standard deviation are the `true' mean and standard deviation of the change in taxable income random walk. For each firm the mean is fixed and the standard deviation is set ranging from low variability to high.

The ratio of the mean ([mu]) and standard deviation ([sigma]) is used to represent the stability of the firm's income flow. For example, a firm with a small ratio of mean to standard deviation is expected to have a higher probability of volatile income streams through time ([sigma] is large relative to [mu]) than a firm whose income stream is stable (ratio close to one). The taxable income volatility will be reflected in variations in the marginal tax rates.

From the forty-year series a starting point (year three) is chosen and the marginal tax rate is calculated for each year for twenty years. (1) The marginal tax rate in time t is defined, as in Scholes and Wolfson (1992), as the present value of the tax rate faced by the firm if an extra $1 of taxable income is added to the current income. In calculating taxable income the statutory tax rate is set at 46%. (2) The discount rate is set to ten percent. The regulations for absorbing losses are varied to allow loss carrybacks and to exclude carrybacks.

In each `firm' the marginal tax rate calculation is repeated for each year to give 1000 parallel marginal tax rate series, based in 1000 generated taxable income series. The average marginal tax rate for each year is then calculated. This average marginal tax rate is taken to be the `true' expected marginal tax rate that the firm faces in each year.

The expected marginal tax rate calculation is repeated for each pair of mean and standard deviation, that is, for each `firm', creating a database of five thousand firm years (twenty data years times 250 `firms'). Hence the simulated data replicates some of the variety found across actual firm histories.

Once the `true' marginal tax rate is calculated for a given firm, a separate single simulated taxable income series (T[I.sub.B]) is realised. This single income stream represents the realised taxable income data observed in firm accounts across time. It is equivalent to the taxable income used by Graham (1996b) for the perfect foresight tax rate. The benchmark marginal tax rate is calculated from the revealed taxable income stream absorbing all losses until exhausted or expired in accordance with the tax regime statutes being applied.

The realised taxable income stream is also used to derive a number of different tax proxies. These proxies are then compared with the `true' marginal tax rate and the benchmark marginal tax rate. (3)

2.1 Simulated Tax Proxy

The first tax proxy is a simulated tax rate similar to that of Shevlin (1990) and Graham (1996b). A taxable income stream is generated starting with the recorded income for year t (4) and projecting forward and back sufficient years to absorb the maximum number of possible loss effects. The projected taxable incomes are generated from a random walk process for change in realized taxable income ([DELTA]T[I.sup.B]) in the same way as the original process described above. However the mean ([[mu].sub.B]) and standard deviation ([[sigma].sub.B]) used to generate the proxy data are those estimated from change in the `realised taxable income' series` Because they are estimates these may be different to the true underlying [mu] and [sigma] parameters. The simulated marginal tax proxy is then formed in the same way as described previously for calculating true marginal tax rates. The process is repeated 40 times for a particular year for each firm.

As noted in the introduction a potential concern with Graham's test of the simulated tax proxy is that it is calculated based on an estimated mean and standard deviation derived from the same realised taxable income stream used to calculate the benchmark marginal tax rate. This could induce a correlation between the simulated and benchmark tax rates that may contaminate evaluations of the simulated proxy. In order to explore this possibility three separate simulated tax proxies are constructed.

The first simulated tax rate is constructed using the entire realised taxable income stream (forty years), designated `simul', to estimate the mean and standard deviation ([[mu].sub.B] and [[sigma].sub.B]) for construction of the simulated tax proxy. Since the simulated rate is based on the entire data set it encapsulates the data used to construct the benchmark marginal tax rate (years three through twenty-two).

A second simulated proxy (rolling proxy), `simulr', is constructed on the mean and standard deviation estimated using the same realised taxable income years that are the basis of the benchmark tax rate. For example when the years three through twenty-two are used to calculate the benchmark marginal tax rate this same set of years is used as the basis for computing the mean and standard deviation ([[mu].sub.B] and [[sigma].sub.B]) for the simulated rate. The proxy is similar to Graham's forward sample (1996b).

The third simulated proxy (`simulgb') uses data that occurs before the taxable income year being assessed, that is, years zero through t-1. This tax proxy has minimal or no overlap with the benchmark marginal tax rate. A comparison of the performance of this non-overlapping proxy with the previous two allows the presence and impact of potential bias. The three proxies are described graphically in figure 1.

[FIGURE 1 OMITTED]

6.2 Other Tax Proxies

Four additional tax proxies are constructed using the simulated taxable income data. (5)

1. The statutory proxy records the statutory rate when present taxable income is positive and records a zero otherwise. This proxy assumes that firms pay tax at the full statutory rate if they have current taxable income and otherwise they pay no tax in the present or future hence the tax rate is zero.

2. The NOL proxy uses the statutory rate when the present taxable income is positive and there are no loss carryforwards and zero otherwise. This proxy operates on a similar assumption to the statutory proxy. However, by explicitly adjusting for the presence of loss carryforwards it incorporates institutional tax details not present in proxy one.

3. The trichotomous proxy (Shevlin 1990) uses the statutory rate when the NOL dummy is the statutory rate and zero when there are losses together with current negative income; however when either present income is positive and there are losses or vice versa the dummy is a half the statutory rate. The trichotomous rate makes an adjustment for the fact that the firm may absorb loss carryforwards in the foreseeable future and again face the statutory tax rate. This possibility is represented by the use of the [[tau].sub.c]/2, an approximation to the present value of future statutory tax payments.

4. Manzon's proxy calculates the marginal tax rate as the present value of the statutory tax rate faced at a future date assuming losses are exhausted within the statutory time. This proxy explicitly addresses the impact of loss carryforwards on future taxable income streams as well as the time value of money impact on present tax liabilities. It assumes that the firm will utilize the losses within the time period allowed by tax legislation.

2.3 Tax Regime Differences

The simulation was repeated under two different tax regimes: 1) the former US tax regime of three years of loss carrybacks and fifteen years of carryforwards; and 2) a regime that has fifteen years of carryforwards and no carrybacks. The alternative regime acts as control to measure the effect of loss treatment difference, carrybacks in particular, on the ability of the tax proxies to measure the underlying marginal tax rate. (6)

3. Methodology

The sample is divided into four subsets. These subsets represent firms with less than seven years to estimate parameters of the taxable income process, firms with greater than seventeen data years for estimation, firms with volatile taxable incomes (measured by the standard deviation of change in taxable income) and stable income firms (with low standard deviations).

For each subsample, two dimensions of tax rate proxies are investigated. First, the ability of each proxy to measure the underlying true marginal tax rate is measured by the [R.sup.2] from regressing the actual marginal tax rate on the alternative proxies.

Second, the possibility that using Graham's benchmark tax rate as the basis for evaluating tax proxies induces a bias toward the simulated marginal tax rate is investigated by calculating correlation coefficients between errors in the benchmark tax rate and errors in the various proxies.

benchmark marginal tax rate - `true' marginal tax rate = error.

proxy marginal tax rate - `true' marginal tax rate = error.

These errors ought to be white noise and uncorrelated with each other. If there were an inbuilt preference between the simulated proxy and the benchmark this would be reflected in correlation between their errors. A t-test indicates whether the correlations are different to zero at the 5% level.

In addition, the relative performance of the simulated tax proxies over the other proxies to explain the true marginal tax rate is measured using incremental [R.sup.2] values from the multivariate regressions.

Actual = [alpha] + [[summation of].sup.k.sub.1][[beta].sub.k] [tax [proxy.sub.k]] + [epsilon]

compared with:

Actual = [alpha] + [[summation of].sup.k.sub.1][[beta].sub.k] [tax [proxy.sub.k]] + [[beta].sub.k] + [sub.1][simulated tax proxy] + [eta]

4. Results

Descriptive statistics for actual and proxy marginal tax rates under both sets of tax regulations are presented in table 1. They reveal that a large percentage of firm year observations have marginal tax rates and proxies equal to the statutory tax rate (0.46). This result is consistent with observed marginal tax rates from historical firm data available on Computstat and raises a potential additional econometric issue. With a large portion of observations having equal (or near equal) values it is possible for a relative few observations to unduly influence regression estimates. To counter this possibility, all regressions were re-estimated with influential observations (7) omitted, yielding no impact on reported results.

Table 1 indicates that the three simulated tax rate proxies have means closer to the actual tax rate and also smaller standard deviations than the binomial proxies do. This is to be expected given the simulated rates are able to capture something of the variation in marginal tax rates not possible with the bimodal proxies. Manzon's proxy also has reduced standard deviation in both tax regimes. However the trichotomous variable in the carryback regime both underestimates the expected value of the actual marginal tax rate and has greater variability.

4.1 Noise and Bias in Marginal Tax Rate Proxies

The correlations of the proxy error (measured as the difference between the actual marginal tax rate and the other variables) are reported in table 2. There is significant correlation between the benchmark error (`erbase') and the errors in the simulated tax proxy (`ersimul') and the rolling simulated tax proxy (`ersimulr') at the 5% level. This suggests that there is an inbuilt bias in the construction of the simulated and rolling simulated tax proxies that improves their apparent performance against the benchmark marginal tax rate. As a result the relative performance of the different tax proxies cannot be compared independently. The simulated proxy constructed from the out-of-sample data (`ersimulgb'), however demonstrates no significant correlation with the benchmark suggesting that it can be compared with the other tax proxies without the presence of bias.

The errors between the non-simulated proxies and the benchmark are statistically uncorrelated. However the errors of these proxies are highly correlated with each other. This is a result of the fact that their construction methods generate similar vectors of marginal tax proxy values. (8)

Table 3 reports summary results for regressions of the `true' marginal tax rate on the various tax proxies as well as the results of the benchmark on the tax proxies. In every case the simulated tax rate is a better measure of the underlying marginal tax rate. From the table it can be also seen that the benchmark is not a particularly good predictor of the actual rates.

From the right hand side panels (regression of benchmark on proxies) in table 3 it can be seen that the bias noted in table 2 between the benchmark and two of the simulated rates has influence on the performance of these proxies (as measured with [R.sup.2]). The non-overlapping simulated proxy (`simulgb'), which does not exhibit correlation in the error with the benchmark, has less explanatory power relative to the rolling proxy (`simulr') in particular.

When loss carrybacks are restricted there is a relative improvement in the explanatory power of the statutory rate proxy, ([R.sup.2] of 83.5 vs. 77.6 with loss carrybacks). Otherwise the results are similar.

The multivariate regression results support the findings set out in table 3. It can be seen from the results in table 4 that each of the simulated tax variables offers significant improvement in explanatory power over the other tax proxies.

4.2 Sample Characteristics and Series Processes

Table 5 presents summary results from the early subset of firms defined as those data points that derive from the first seven data years in the simulation.

The performance of the simple proxies relative to the simulated proxies is reduced in this subset.

The income volatility subsets (table 6) demonstrate superior performance for the simulated proxy over the other proxies ([R.sup.2] is a minimum of 10% better than other proxies in explanatory power under both tax regimes). Firms with volatile taxable income streams exhibit greater variation in marginal tax rates.

These results support the suggestions of earlier papers that when taxable income streams are highly variable it is best to use a tax proxy that captures and reflects that variation.

Overall the results of this study support the simulated tax proxy as capturing the variability of the underlying actual tax series well. (9) However, sometimes the difference between the simulated proxy and the next best alternative is small. This factor needs to be considered when the decision is being made whether or not a simulated proxy is to be constructed.

5. Conclusion

The results of this simulated test of relative tax proxy performance indicate that there are some important areas for consideration by researchers when constructing tax proxies. Firstly, if a simulated proxy is constructed in a manner similar to that of Graham, then the use of the same data to construct the proxy and another variable of interest may result in a more favorable result for the tax proxy. This is reflected in the correlation between the errors in the benchmark tax rate and two of the simulated tax proxies. The use of out-of-sample data needs to be considered in such cases.

However, if the sample under study is small, the lack of out-of-sample data may be problematic. The two issues of variable bias and small sample size need to be weighed against each other in these situations.

The results of the subset analysis suggest that different proxies will perform better under different conditions. The simulated proxy is particularly good to capture variability in marginal tax rates. However in situations where there is stability in tax rates another proxy that is easy to construct will do almost as well. Manzon's proxy in particular appears to provide an unbiased estimate and outperforms the other simple proxies.

The simulated tax proxy can be time consuming to construct using actual data and requires access to accounting data in order to reconstruct the underlying taxable income. Depending on the accounting policies and the data available some of the figures needed for this task may not be available or may be measured with a significant error. If this is the case the performance of the simulated proxy would be compromised and another proxy less dependent on this construction may be suitable and give robust results.

The findings of this study suggest that there is still work to be done to evaluate the relative ability of tax proxies to capture the underlying associations between tax effects and other variables of interest in corporate finance research. Such areas include using actual data and assessing the importance of other institutional details that impact on marginal tax rates

(1.) The simplified simulated time series is constructed in similar fashion to Graham's forward sample, for example with US tax treatment each year of marginal tax rates is constructed assuming three prior years of tax carrybacks and 15 future years of tax carryforwards. Year 3 is taken as the first year to allow for carryback of losses to be implemented, if necessary, under the US tax regime.

(2.) The 46% tax rate is in keeping with the US statutory rate before the 1986 tax changes. To this end it mirrors the assumptions forming part the studies of Shevlin, 1990 and Graham 1996. Likewise 3 years of loss carrybacks and 15 year carry forwards was the system current in the US until August 5th 1997 and hence is the system current contemporaneously with the 46% tax rate. Similarly, in Australia the tax rate has changed a number of times in the last ten years.

(3.) Since the simulation used here generates taxable income rather than reconstructing it from accounting data it is surmised that the simulated taxable income stream is less noisy than one reconstructed from actual accounting data. Subsequently, the derived tax proxies will also be less noisy since tax proxies are a function of taxable income. As a consequence it is expected that the results based on the simulated data will be stronger than those on the basis of reconstructed income series would be.

(4.) Under a tax regime with tax loss carrybacks the years relating to the carrybacks are included in the evaluation of the tax proxy.

(5.) Graham (1996b) also investigated several additional tax proxies based on accounting data. These are not studied here since the required data are not easily incorporated into the simulation model used.

(6.) This comparison based on the presence or absence of carrybacks is of interest since many countries do not allow tax carrybacks but will allow carryforwards of losses over varying time periods. Further under a no carryback regime the NOL, statutory and trichotomous proxy collapse into a single measure, the statutory rate proxy.

(7.) Defined by hi>3p/n, where hi is the ith observation in the hat matrix, p is the number of predictors plus one and n is the number of observations.

(8.) This is extreme under the no carryback regime where the statutory, trichotomous and NOL proxies are the same.

(9.) The results presented in the body of the paper are built on the assumption that the generating function is a random walk. An alternative generating process, which has been documented by Brooks and Buckmaster (1980) and Shevlin (1990), is mean reversion. In order to test the sensitivity of the results reported here to the assumptions of random walk the simulation is repeated on the basis of `true' taxable income being a mean reverting process. The process simulated is; T[I.sub.it] = [[mu].sub.i] + p(T[I.sub.it-1] - [[mu].sub.i])+[[epsilon].sub.it], where

TI,[mu] and c are as previously and p is an autoregressive parameter. A fixed value of 0.48 is chosen for p. This value is the median value observed by Shevlin (1990) in his data series and represents a reasonable degree of autoregressive behavior where impacts of the mean reversion would be expected in the results of the simulation if there is sensitivity to the time series process. The analysis was also performed with values of p of 0.96, 0.89 and 0.20. All gave similar results to the 0.48 value. The results of the tax proxy performance across the whole sample remain unchanged in terms of ranking.

Table 1
Descriptive Statistics for US Regulations Tax Series and Non-US
Regulations

  Variable      Mean     Median    Standard       First
N = 5000 (a)                       Deviation   Quartile (b)

               Panel A: US Tax Regime Loss Carrybacks in
                                 Use

actual         0.35107   0.46000     0.16803     0.23300
base           0.35049   0.45900     0.18036     0.26000
simul          0.34769   0.46000     0.17265     0.23200
simulgb        0.33613   0.46000     0.18688     0.16100
simulr         0.35088   0.46000     0.16898     0.25425
stat           0.31050   0.46000     0.21547     0.00000
NOL            0.32494   0.46000     0.20951     0.00000
Manzon         0.35953   0.46000     0.15624     0.12100
tric           0.31772   0.46000     0.20869     0.00000

                  Panel B: Non-US Tax Regime No Loss
                            Carrybacks

actual         0.34827   0.46000     0.17074     0.20725
base           0.34711   0.45900     0.18171     0.26000
simul          0.34489   0.46000     0.17570     0.20100
simulgb        0.33324   0.46000     0.18966     0.13400
simulr         0.34852   0.46000     0.17213     0.22325
stat (c)       0.30406   0.46000     0.21777     0.00000
Manzon         0.34399   0.46000     0.16242     0.11000

Note: (a) The 5000 data points are comprised of data for 250
companies through 20 years each.

(b) Since the median value under both regimes is the statutory
rate of 0.46 the third quartile values are not reported, they
are all 0.46 the statutory rate.

(c) Under the no carryback regime the statutory proxy, NOL proxy
and trichotomous proxy are equivalent.

actual = the actual expected marginal tax rate usually unknown
to researchers;

base = the benchmark marginal tax rate derived from the realised
stream of taxable incomes;

simul = the simulated marginal tax rate using the full 40 years
of actualised taxable income for the moments;

simulgb = the simulated tax rate using non-overlapping data from
the realised income series;

simul r = the simulated tax series that is based on the taxable
income series matching the benchmark income series;

stat = the statutory proxy;

NOL = the NOL proxy;

Manzon = Manzon's proxy; and

tric = the trichotomous proxy.

Table 2
Correlations Between the Errors in Measurement for the
Benchmark and Proxies from the Actual Tax Series *

Errors are constructed as:
benchmark - actual = error; or proxy - actual = error

             erbase   ersimul   ersimulgb   ersimulr

erbase                 0.335      0.002      0.484
                      (0.00)     (0.879)    (0.00)
ersimul       0.368               0.305      0.755
             (0.00)
ersimulgb    -0.011    0.316                 0.039
             (0.437)
ersimulr      0.542    0.753      0.049
             (0.00)
erstat (a)    0.018    0.201      0.536      0.053
erNOL          -        -          -           -
erman          -        -          -           -
ertric         -        -          -           -

             erstat    ErNOL      erman     ertric

erbase       -0.021   -0.012     -0.026      -0.019
ersimul       0.096    0.086     -0.006       0.100
ersimulgb     0.407    0.533      0.294       0.508
ersimulr     -0.014   -0.063     -0.016      -0.039
erstat (a)             0.657      0.484       0.929
erNOL          -                  0.76        0.889
erman          -        -                     0.666
ertric         -        -          -

Note: * The Upper RH section represents the US tax regime
and the lower LH section the no carryback tax regime.

(a) Under the no carryback regime these four proxies have
the same errors and hence the same correlations as the
`erstat' variable. They are therefore perfectly correlated
with each other.

erbase = the difference between the actual marginal tax rate
and the benchmark marginal tax rate;

ersimul = the difference between the simulated proxy using
the full 40 data years and the actual;

ersimulgb = the simulated tax proxy using out-of-sample data;
and `ersimulr' is the tax proxy based on the data used to
construct the benchmark tax series.

erstat = the error between the statutory tax proxy and the
actual tax series;

erNOL = based in the NOL proxy;

erman = the difference between Manzon's proxy and the actual
tax series; and

ertric = the trichotomous approximation errors from the actual
tax series.

P values are given at the 5% confidence interval that the
correlation is zero for the correlations between the benchmark
error and the three simulated errors. These show that the
correlation between the `simul' proxy and the `simulr' proxy are
strongly positive evidencing bias between these variables and
the benchmark.

Table 3
Regression Results of Actual Tax Rate and Benchmark Tax Rate
Against Tax Proxies Under Both Tax Regimes

                Actual MTR= [alpha] + [beta]proxyMTR
                            + [epsilon]

                          [[beta].sup.   [R.sup.2]
                [alpha]   ([section)]]

                Panel A: US Tax Regime Loss Carrybacks
                             in Use

benchmark         0.045        0.847       87.9
                            (190.87)
simul             0.015        0.965       98.4
                            (556.64)
simulgb           0.054        0.883       96.4
                            (363.80)
simulr            0.009        0.976       96.4
                            (365.56)
statutory         0.138        0.687       77.5
                            (131.36)
NOL               0.110        0.741       85.4
                            (171.26)
Manzon           -0.01         1.01        87.4
                            (186.22)
trichotomous      0.116        0.740       84.4
                            (164.30)

                Panel B: Non-US Tax Regime No Loss
                           Carrybacks

benchmark         0.04         0.889       89.6
                            (207.51)
simul             0.015        0.965       98.6
                            (597.72)
simulgb           0.053        0.885       96.8
                            (385.83)
simulr            0.008        0.976       96.9
                            (395.2)
statutory (a)     0.13         0.716       83.5
                            (159.06)
Manzon            0.014        0.972       85.5
                            (171.67)

                   Benchmark MTR= [alpha] +
                    [beta]proxyMTR + [eta]

                [alpha]   [[beta].sup.   [R.sup.2]
                          ([section])]

                Panel A: US Tax Regime Loss Carrybacks
                          in Use

benchmark

simul            0.0073        0.987       89.3
                            (204.22)
simulgb          0.0520        0.888       84.7
                            (166.16)
simulr          -0.006         1.02        90.8
                            (221.69)
statutory        0.137         0.688       67.5
                            (101.87)
NOL              0.109         0.744       74.7
                            (121.53)
Manzon          -0.0123        1.01        76.4
                            (127.19)
trichotomous     0.115         0.742       73.6
                            (118.09)

                Panel B: Non-US Tax Regime No Loss
                          Carrybacks

benchmark

simul            0.0068        0.987       91.0
                           (22.5.05)
simulgb          0.0503        0.891       86.4
                            (178.58)
simulr          -0.0071        1.02        92.7
                            (251.4)
statutory (a)    0.127         0.723       75.1
                            (122.71)
Manzon           0.0099        0.98        76.8
                            (128.62)

Note: ([section]) t stat in brackets for 5% confidence
interval; and

(a) Under the no carryback regime the statutory proxy,
NOL proxy and trichotomous proxy are equivalent.

Table 4
Regression Results for Multivariate Regressions of All Tax Proxies
to Demonstrate the Incremental Explanatory Power From the Three
Simulated Tax Proxies Over the Other Proxies Examined

                Actual MTR = [alpha] + [Zigma]
              [beta]proxyMTR + [[epsilon].sup.([section])]

                A          B          C         D

              Panel A: US Tax Regime Loss Carrybacks in
                                Use

intercept      -0.227     -0.009     0.063    -0.057
statutory       0.124      0.003    -0.001     0.020
               (8.467)    (0.711)   (0.258)   (3.12)
NOL            -1.51      -0.119    0.0556    -0.341
               (8.607)    (2.55)    (1.152)   (4.95)
Manzon (b)      2.862      0.264    -0.082     0.697
              (12.353)    (3.95)    (1.11)    (7.17)
simul           --         0.872     --        --
                        (100.88)
simulgb         --         --        0.891     --
                                   (65.03)
simulr          --         --        --        0.747
                                             (67.73)
[R.sup.2]      89.2       98.54     96.36     97.29

                Actual MTR = [alpha] + [Zigma]
               [beta]proxyMTR + [[eta].sup.([section])]

                A          B          C         D

              Panel B: Non-US Tax Regime No Loss
                         Carrybacks

intercept      -0.194      0.008    0.0748    -0.029
statutory      -1.33      -0.035    0.114     -0.198
             (-23.6)     (-1.82)   (3.74)    (-7.29)
NOL

Manzon (b)      2.76       0.0873  -0.209      0.431
              (36.36)     (3.15)  (-4.68)    (11.15)
simul           --         0.93     --          --
                        (207.16)
simulgb         --         --       0.932      --
                                 (123.47)
simulr          --         --       --         0.831
                                            (137.4)
[R.sup.2]      86.9       98.6     96.8       97.3

Note: A multivariate regression of actual tax rate regressed
on the simple tax proxies: statutory (`stat'), `NOL' and
Manzon's proxy (Column A).

Subsequent regressions estimate the
incremental value contributed by each of the three simulated tax
proxies in turn (columns B, C and D).

These regressions are executed under both loss treatment scenarios.

(a) Under the no carryback regime the statutory proxy, NOL proxy
and trichotomous proxy are equivalent;

(b) The trichotomous variable is not included in the multivariate
analysis as it is perfectly correlated with statutory and NOL
variables; and

([section]) t stat in brackets for 5% confidence interval.

Table 5
Regression Results for the Small Sample Firms Subset Under Both
Sets of Tax Regulations

               Actual MTR= [alpha] + [beta]proxyMTR
                          + [epsilon]

               [alpha]   [[beta].sup.   [R.sup.2]
                         ([section]])

               Panel A: US Tax Regime Loss Carrybacks
                             in Use

benchmark        0.068        0.793       79.3
                            (69.25)
simul            0.012        0.952       96.9
                           (197.01)
simulgb          0.098        0.779       92.6
                           (125.26)
simulr           0.022        0.937       93.0
                           (129.17)
statutory        0.181        0.578       70.5
                            (54.61)
NOL              0.145        0.647       82.4
                            (76.38)
Manzon           0.046        0.863       83.3
                            (79.07)
trichotomous     0.153        0.649       80.9
                            (72.72)

                   Actual MTR =  [alpha] +
                  [beta]proxyMTR + [epsilon]

               [alpha]   [[beta].sup.   [R.sup.2]
                         ([section])]

               Panel B: Non-US Rax Regime No Loss
                           Carrybacks

benchmark        0.103        0.6537      80.9
                            (48.08)
simul            0.052        0.881       97.5
                           (128.15)
simulgb          0.094        0.792       93.4
                           (133.3)
simulr           0.021        0.941       94
                           (140.21)
statutory        0.167        0.637       81.9
                            (75.17)
NOL
Manzon           0.07         0.85        83
                            (77.99)
trichotomous

Table 6
Regression Results for the High Volatile Taxable Income Firms Sub
Set Under Both Sets of Tax Regulations

               Actual MTR= [alpha] + [beta]proxyMTR
                         + [epsilon]

               [alpha]   [[beta].sup.   [R.sup.2]
                         ([section]])

               Panel A: US Tax Regime Loss Carrybacks
                             in Use

benchmark        0.036        0.861       86.3
                            (93.31)
simul            0.004        0.984       98.6
                           (312.4)
simulgb          0.027        0.933       97.8
                           (248.2)
simulr          -0.00         0.988       96.4
                           (191.29)
statutory        0.096        0.759       79.1
                            (72.27)
NOL              0.074        0.785       86.6
                            (94.46)
Manzon          -0.05         1.07        88.6
                           (103.6)
trichotomous     0.078        0.807       86
                            (92.05)

                    Actual MTR= [alpha] +
                  [beta]proxyMTR + [epsilon]

               [alpha]   [[beta].sup.   [R.sup.2]
                         ([section])]

               Panel B: Non-US Rax Regime No Loss
                         Carrybacks

benchmark       0.03          0.887       88.5
                           (102.9)
simul           0.004         0.987       98.8
                           (336.5)
simulgb         0.027         0.94        97.9
                           (255.88)
simulr         -0.00          0.99        96.9
                           (208.07)
statutory       0.093         0.798       84.6
                            (87.19)
NOL

Manzon          -0.04         1.08        87
                            (96.14)
trichotomous

This paper is drawn from my PhD dissertation at the University of NSW. I am grateful to Greg Clinch of MBS, Doug Foster, Baljit Sidhu, Tom Smith and Garry Twite of AGSM, John Graham of Duke University, and Kim Sawyer of University of Melbourne for comments and suggestions. All errors and omissions are my own.

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(Date of receipt of final transcript: October, 2002. Accepted by Garry Twite, Area Editor.)

Kerry Pattenden, School of Business and Economics, Sydney University, Sydney NSW 2006. Email: [e-mail]