Learning Theory and Equity Valuation : An Empirical Analysis

This paper tested the Pástor and Veronesi (2003) hypothesi s that the market-to-book ratio (M/B) is negatively related to the number of years (age) duri ng which a firm has had its stock traded on an Exchange. The predicted decline takes place as a result of a learning process by investors. The authors tested this implication in the U.S . market using the Fama and MacBeth (1973) methodology. In the present article a more ge neral econometric approach is adopted, with the use of panel data and fixed-factor regres so s, with data for stocks traded at the São Paulo Stock Exchange (BOVESPA). The evidence doe s not reject the Pástor and Veronesi hypothesis. Additional conjectures were tested r egarding the learning process. These tests indicate that the greater availability of data o n company amplifies the effect of the age variable on the M/B ratio, implying a more accelerate d learning process. This paper concludes that the evidence for the Brazilian market suppor ts the theory that investors learn.


Introduction and Objectives
Predictability and excess volatility involving stock returns are topics of major concern in the finance literature.These empirical anomalies contradict the efficient market and rational investor hypotheses that are basic to several pricing models.The learning literature attributes the occurrence of such phenomena to parameter revision by rational agents in their dividend forecasting models.Pástor and Veronesi (2003) have developed a model that relates learning concepts to equity valuation.One of the model's implications is that the market-to-book (M/B) ratio is positively related to the uncertainty about a firm's future profitability.Since that uncertainty declines over time, thanks to the learning effect, the model predicts that a younger firm should have a higher M/B ratio than an identical, albeit older firm.
The authors tested that implication using the Fama and MacBeth (1973) procedure with annual data for listed companies in the U.S. market, covering the 1962-2000 period.The results confirmed the model's predictions.
The objective of the present article is to test the implication of the Pástor and Veronesi (2003) model for the effect of age on the M/B ratio using data for companies listed at the BOVESPA.However, a different econometric procedure is adopted.Panel data models are used, in such a way as to incorporate firm-specific effects and time-series effects on all sample data.Additional conjectures are proposed and tested regarding the learning process.
The article is structured as follows: in the next section, a review of the literature is presented, and this is followed by a discussion of the econometric methods used.Section 4 presents the data and their descriptive statistics.Section 5 presents the test results.Section 6 extends the empirical analysis to conjectures on the learning process, while section 7 contains the article's conclusions.

Literature Review
According to Fama (1970), an efficient market is that in which current prices reflect all available information.This implies that, whatever expected return model is used, the information available at that moment is fully utilized in the determination of equilibrium returns.A market in which (i) there are no transactions costs, (ii) all agents have costless access to complete information, and (iii) all agents agree as to the implications of such information for the prices of all assets, is certainly an efficient market.These conditions, while sufficient, are not necessary for market efficiency, i. e., their absence does not automatically lead to the market inefficiency, but may be a cause of inefficiency. 1he most significant implication of the efficient market hypothesis is the impossibility, on the basis of currently available information, of setting up an investment strategy that will produce above-equilibrium returns.
A complementary hypothesis is that of rational expectations.According to Copeland et al. (2003), the rational expectations hypothesis predicts says that asset prices are determined by their expected cash flows.Thus, a market with rational expectations is an efficient market, since prices will reflect all existing information.
The most widely known expect return model, both among academics and market practitioners, is the Capital Asset Pricing Model (CAPM), developed by Sharpe (1964), Lintner (1965) and Black (1972).For the purposes of this paper, the main predictions are: (i) an asset's expected return is linearly related to its beta (its measure of non-diversifiable risk), (ii) beta is sufficient for explaining contemporaneous return differences in a sample of assets.
However, there is ample literature providing empirical evidence of return predictability and excess volatility, that is, facts that contradict the efficient market and rational investor hypotheses, as well as CAPM implications.
For example, Fama and French (1992) obtained evidence, for the 1963-1990 period, indicating that returns for U.S. stocks are strongly correlated with size, as measured by market capitalization (M) and with the book-to-market ratio (B/M), and weakly correlated with beta Fama andFrench (1993, 1996) suggest that the anomalies not explained by the CAPM can be captured by a three-factor model including: (i) the excess return on the market portfolio relative to the return on the risk-free asset; (ii) the difference between the returns on a low market value stock portfolio and the returns on a high market value stock portfolio ("size effect"); and (iii) the difference between the returns on a high book-to-market ratio stock portfolio and the returns on a low book-to-market ratio stock portfolio ("value effect").Jegadeesh and T. (1993) present evidence for the U.S. market, using a 1965-1989 sample, indicating that strategies long on winners and short on losers in the 3-12 preceding months provide abnormal returns for one year after the construction of the corresponding portfolios.LeRoy and Porter (1981) and Shiller (1981) argue that stock price volatility is much higher than would be justified by changes in expectations regarding future dividends.Shiller computed the upper bound for stock return volatility given by the efficient market hypothesis.He found evidence indicating that the volatilities of the Standard and Poor's 500 index and the Dow Jones Industrial Average were more than five times above that upper bound.This comparison covered the 19871-1979 period for the Standard e Poor's 500 index, and the 1928-1979 period for the Dow Jones Industrial Average.The author argues that the difference is too large to be explained by measurement errors, index composition problems, or tax legislation changes.
provided investors had more information, or, in the sense of this article, had had ample time to learn more about the particular firm.We thank an anonymous referee for pointing this out to us.
According to Brav and Heaton (2002), two major theoretical approaches have emerged as explanations for such anomalies.The first one uses behavioral factors to relax the assumption that investors process information in a fully rational manner.In behavioral theories, investors suffer from cognitive biases and, although they know the economy's fundamental structure, they act irrationally.
The second theoretical approach, the so-called structural rational uncertainty approach, preserves the rationality assumption, but relaxes the assumption that agents have complete knowledge of the economy's fundamental structure.This approach explores the distinction between rational expectations and rational investors.In a rational expectations environment, rational investors make statistically optimal decisions in a world in which they possess all relevant structural information.Outside the realm of rational expectations, investors still make statistically optimal decisions, but do not have full knowledge of the economy's structure.
For example, even when an investor knows that a firm's profitability follows a mean reversion process, he/she will not have access the true value of the reversion parameter, and his/her decisions will be based on estimates.If the economy's parameters were constant over time, the learning process would eliminate financial anomalies.Brav and Heaton (2002) compare the two theoretical approaches emphasizing deviations relative to the rational expectations hypothesis.They examined simple models in which representative investors must estimate unknown relevant parameters in order to determine an asset's intrinsic value.In the behavioral approach, investors display a conservative bias or give large weight to the more recent data.In the structural rational uncertainty approach, investors adopt bayesian techniques when estimating parameters.The focus of their analysis is in the overreaction and underreaction phenomena.They conclude that, even though different hypotheses had been relaxed, the mathematical and predictive similarities of the two models make it impossible to distinguish one from the other.Timmermann (1993) uses the structural rational uncertainty and learning approach to present the intuition for the occurrence of excess volatility and return predictability.
Consider a rational agent using least square techniques to estimate dividend growth rates, and that the agent obtains an average growth estimated below the true growth rate.Therefore, the stock price will be lower than its intrinsic value, since the first is equal to the present value of expected dividends.The subsequent dividend payment will produce a high rate of return for the investor, for two reasons: (i) the dividend yield (dividend/stock price) will be high due to the low stock price; and (ii) the revision of the average growth rate of future dividends will result in the stock's appreciation.This dynamics will result in positive correlation between dividend yield and stock returns.
As to the effect on volatility, Timmermann (1993) considers a dividend shock in order to assess the implications of a rational expectations model against those of a model with learning.In the rational expectations model, stock prices are proportional to dividends and, hence, the dividend shock will be transmitted as a proportional price shock.Learning implies an additional effect on stock price, since the estimate of the average dividend growth rate is also influenced by the dividend shock.Using simulation, Timmerman finds evidence for the generation of statistically significant correlations between dividend yields and future returns by the learning effects.In the meantime, excess volatilities are observed only in small samples, since, as sample size increases, the estimated parameter converges it its true value.This ends up reducing the effect of learning on volatility.Lewellen and Shanken (2002) argue that tests of market efficiency are unable to distinguish between a market with learning and an irrational market.They demonstrate that the empirical properties of returns may diverge significantly from those perceived by investors, even when the efficient market and rational investor hypotheses are valid.In other words, returns may be predictable even when investors perceive a constant risk premium; prices may seem excessively volatile, even though investors make rational decisions; and the CAPM may be incapable of describing returns, even though investors choose portfolios with mean-variance criteria.In spite of these empirical anomalies, investors are incapable of profiting from them, since they never know whether past dividends are above or below their true value.However, as time passes, investors learn more about expected dividends, correct their past mistakes and the stock price converges to its fundamental value.
In an addition to Fama (1970), which argues that empirical tests of asset pricing models involve a joint hypothesis of market efficiency and expected return model, Lewellen and Shanken (2002) suggest that such tests require an additional hypothesis about investors' prior beliefs.Pástor and Veronesi (2003) have developed a stock pricing model that takes into consideration the effects of learning on parameter estimation, and have obtained the following implications:2 • The market-to-book ratio (M/B) is directly proportional to the firm's expected profitability (net income/net worth) and inversely proportional to the stock's expected return, in line with the existing literature.Furthermore, the M/B multiple is positively related to the variance of investor expectations regarding average net worth growth.Since this growth is equal to net income/net worth (profitability) minus dividends/net worth, the M/B multiple is also positively related to the uncertainty of future profitability, and this effect is more pronounced in the case of non-dividend paying firms.(See Figure 1 in Pástor andVeronesi (2003, p.1757).
• Idiosyncratic return volatility increases with uncertainty about the firm's average future profitability.(See lower panel of Figure 3 in Pástor andVeronesi (2003, p. 1762).
• Since uncertainty about future profitability decreases over time, thanks to the learning effect, the model predicts that a younger firm will have higher M/B multiple and stock volatility than those of older firms, after other stock-value determining firm characteristics are controlled for.(See Figure 4 in Pástor andVeronesi (2003, p. 1763)).
• The M/B ratio declines and converges to one in the long-turn, with the passage of time, or, in other words, the older the firm, since a firm, as a member of a particular sector, will live through that sector's product life cycle.One characteristic of the transition from introduction to growth, stability, maturity and decline is, naturally, the reduction in returns on equity, with the drying up of profit opportunities.
The intuition for the relationship between the variance of investor expectations and the M/B ratio is associated with the convexity of the relationship between asset value and growth rate.Consider, for example, an asset with a face value equal to 100, maturing 10 years from now and an unknown growth rate.Assume that the minimum rate of return required by an investor for an asset in this risk class is equal to 10% per annum.Each investor will have to estimate the average growth rate for the next 10 years in order to determine the asset's fair value.Exhibit 1 illustrates the value of the asset for estimated growth rates ranging between 2% and 30% per annum.

Figure 1
Exhibit 1 -Asset present value as a function of growth rate For each annual growth rate, the solid line represents the present value of a hypothetical asset with face value of 100 and 10 years to maturity.The present value is computed with a 10% annual discount rate.The dotted line represents the average of present values calculated with all growth rates.The dashed line represents the average of present values calculated with the minimum and maximum growth rates.The dash-and-dot line represents the present value of the asset calculated with a growth rate equal to the average of all growth rates, namely, 16%.
If all investors estimed the growth rate as the average between 2% and 30% per annum, that is, 16% per annum.The asset's expected value would be equal to 170.This is the situation in which the variance of investor expectations is equal to zero.At the other extreme, if 50% of all investors used a 2% growth rate, and the remainder used a 30% growth rate, that is, maximum investor expectation variance, the asset's expected value would have been equal to 289.This illustrates the effect of investor expectation variance on the asset's expected value: the greater the variance, the higher the asset value.
In turn, expectation variance declines with time, due to the learning process.This implies that, the older the firm, that is, the longer the firm stock has been traded on the exchange, the lower is the variance of investor expectations, and this results in a lower market value, all other things constant.Pástor and Veronesi (2003) tested the implications of their model with data for exchange-listed U.S. firms, using annual data for the 1962-2000 period.They used the Fama and MacBeth (1973) procedure, that is, least square regression models were estimated with cross section data and inferences were made regarding the mean values of computed coefficients in the various years in this period.The results confirmed the model's predictions.In the regression of M/B against the firm's age and control variables, the coefficients of the age variable are negative and statistically significant.Evidence was also obtained for a stronger effect of age in non-dividend paying firms, as well as for a negative and statistically significant relationship between idiosyncratic volatility and the firm's age.Pástor and Veronesi (2003) used the following model to test the implications for the M/B multiple in each annual cross section:

Econometric Methods
where: N is the number of firms with valid date in current year t; a is a constant; q refers to the number of years ahead.In the current year t, q = 0; Q is the maximum number of ex-post terms estimated; DD is a dummy variable which takes the value 1 in the years the firm paid dividends; LEV is financial leverage, measured by total debt divided by total assets in year t; SIZE is the natural logarithm of total assets in year t; V OLROE is the residual variance of an AR(1) process for each firm's ROE with a minimum history of 10 years; ROE is return on equity, computed as the ratio of net income in t + q to net worth in t + q; RET is the stock's total return (dividends plus price change) in t + q.
The AGE variable was defined as the negative of the reciprocal of one plus the firm's age: − 1 1+age .This specification was adopted by Pástor and Veronesi (2003) on the basis of the functional form resulting from their model, relating age to uncertainty as to future profitability.In this context, age is the number of years for which the firm has had stock listed on the exchange.
According to Pástor and Veronesi (2003), stocks' future returns (RET) and future profitability (ROE) are proxies for controlling for expected returns and expected profitability.With rational expectations, these variables are reasonably well captured by ex post observed values.VOLROE, LEV and SIZE complete the set of control variables that may affect the values of M/B.
The testing procedure adopted by Pástor and Veronesi (2003) assumes that the samples are randomly obtained in each period and, therefore, that the cross sections are independent.This means that firm individual characteristics are not considered.However, the observed data in each period are not independent.In other words, each year's cross section is obtained with the same firms, with the exception of those included in the sample because their market values are observed for the first time in that year, as well as those that have left the sample because they are no longer listed.
The panel approach is the most appropriate in this case, since it makes it possible to include an individual specific effect (c i ); in other words, it is possible to consider, in the estimation process, all characteristics which are intrinsic to each firm and that do not change over time.This is a more general specification than a previous specification, whose only time-invariant characteristic was the VOLROE variable, standing for profitability volatility.The present approach also allows us to exclude the RET variable.Assuming rational expectations, that is, assuming that ex post returns are the returns predicted ex ante by investors, the cross section variation in terms of expected returns must be explained by the riskiness of each firm.When we remove returns from the structural model, we are assuming that each firm's risk, as well as its risk premium, are constant over time and may thus be captured by the specific effect estimated for each firm.
Hence, the panel estimation is based on the following structural specification: where: c i is each firm's specific effect; T is the total number of years in the sample; DummyY ear is a dummy variable for each sample year, taking on the value of 1 when k = t and 0 when k = t.This more general approach eliminates the possibility of specification bias due to variable omission, since all factors not explicitly considered in the structural specification are accounted for by each firm's specific factor, c i , and by the year dummy variables.
In addition, it is reasonable to assume that c i is correlated with the other independent variables, that is, that time-invariant and specific characteristics of each firm, such as management style and organizational culture, are associated with, for instance, its profitability (ROE) and leverage (LEV).This means that the estimation procedure used by Pástor and Veronesi (2003) may suffer from an omitted variable bias which, according to Wooldridge (2003), is sometimes referred to as an heterogeneity bias.
Given the assumption of correlation between the specific effect and the other independent variables, the most adequate estimation procedure is fixed-effect estimation.
Two additional assumptions are required for the unbiasedness and efficiency of fixed-effect estimators: (i) homoscedastic and uncorrelated error term, u it and (ii) independent variables are strictly exogenous.According to Wooldridge (2003), if u it follows a random walk process, then the fixed-effect estimator will be less efficient, and a better alternative would be to use the first-difference estimator.The assumption of stationary u it is in accordance with the literature and the nature of the variables involved, shocks of which tend to dissipate with the passage of time and, in a few cases, exhibit mean reversion.For example, see Fama and French (2000) and Penman (1991).The assumption of i.i.d.errors is too strong for the data in question.Thus, inferences presented in sections 5 and 6 are made on the basis of Huber-White robust estimators for both heteroscedasticity and serial correlation, implemented in the Stata software according to Rogers (1993).
Regarding assumption (ii) above, results will be presented for the endogeneity test involving the AGE variable, the variable of interest in our inferences.

Database and Descriptive Statistics
We used the Economática database, containing financial accounting information for the 1995-2006 period, as well as market value and net worth from 1986 to 2006.The most important implication from the model is that the uncertainty regarding profitability is reduced over time thanks to the learning process, and this reduces the market value/net worth multiple.Therefore, a relevant piece of information is the date of initial listing of shares of stock by the firm on the exchange.From this date on, the firm must publish its accounting statements, even if its stock is not traded on the exchange.Hence, even if a firm distributes new shares several years after becoming listed, investors will have access to the history of information on the firm, enabling them to learn about its fundamentals and use this knowledge to price the stock.
The market entry date for a firm was defined as the year in which its stock quotation series started in the Economática database.However, since the Economática database itself begins in 1986, for the firms that started trading at the Bovespa before 1986, their original listing date at the exchange was collected from the Bovespa annual reports.This is how the AGE variable was measured, as the number of years from the original listing date or the beginning of price series in the database, whichever was the earliest.3
In order to ascertain whether size growth could be a sign of survivorship bias, the following analysis was performed: in 1999, there were 169 firms, of which 106 survived until 2006, the last sample year.These firms, in turn, amount to 72% of the firms for which data are available in 2006.During this seven-year window, a nearly 25% renewal of the sample has taken place.If one considered the firms included in the first sample year (1995), these would represent only 33% of the firms present in the 2006 sample.Therefore, the continued asset growth may be attributed to market and macroeconomic forces, leading to the increase in the average size of firms whose stock are listed at the exchange.
Table 2 contains the correlation coefficient matrix for the variables.In addition to the dependent variable and the regressors included in structural model (2), the table includes two other variables: a dummy variable for the existence of ADRs (ADR) and the AssetGrowth variable, defined as a truncated variable taking on the value of zero if the absolute value of change in total asset is at most 50%, and equal to the percentage change in total assets if this is above 50%.Both variables are discussed in section 6.It may be observed that M/B is negatively correlated with AGE; although this is significant at the 5% level, the absolute value of the coefficient is small (-0,06).The strongest correlations are between SIZE and ADR (0,42), M/B and SIZE (0,30), and M/B and ADR (0,23).
In Exhibit 2, the observations were classified into eight groups, according to the firm's age, and each group contains from 198 to 239 observations.For each group, the means and medians of M/B were calculated.It may be noticed that both the mean and the median decline as far as the 8-10 year group.From this point on, the mean of M/B increases with age, in contradiction with the hypothesis of a decline in M/B with age.

Empirical Analysis
The variable of interest for inference in the empirical analysis is AGE.Thus, in order to prevent the possibility that estimates are biased as a result of endogeneity, the Durbin-Wu-Hausman test, as described by Heij et al. (2004), was performed.For that purpose, instruments were defined by regressions of AGE against lagged values of M/B and the other regressors in structural model (2).Regarding the instruments selected, the Sargan exogeneity test was applied, as described in Heij et al. (2004).The entire procedure was used both with fixed-effect and randomeffect estimators.The results do not reject the null hypothesis of exogeneity for AGE in the fixed-effect regression, as detailed in Table 3.This evidence confirms that the use of fixed-effect panel estimation is more appropriate for making inferences regarding the AGE variable.The results obtained in the estimation with structural model (2) are presented in Table 4.In all regressions, we used robust variance estimators, as discussed in section 3. Pástor and Veronesi (2003) estimated results for Q = 0, 1, 5, 10, 15, 20 and 25.However, due to the limited data history, we used Q = 0, 1 and 2.
The hypothesis being tested is whether the coefficient of AGE is significantly different from zero and negative.This hypothesis comes from the implication of the Pástor and Veronesi (2003) model that uncertainty about future profitability, represented by AGE, decreases with time, and this is reflected on a lower M/B ratio.
Formally, the tested hypothesis is: The coefficient of the AGE variable was negative and significant at the 1% level in all specifications considered.Therefore, there is evidence for rejecting the null hypothesis.In other words, it is not possible to reject the contention that the M/B ratio has a negative relationship with the length of the period during which a firm's stock has been traded at the exchange, as predicted by Pástor and Veronesi (2003).In the Age column, the logarithm of the M/B ratio is initially regressed against the firm's AGE (number of years since initial exchange listing).In the remaining columns, the logarithm of the M/B ratio is regressed against AGE, and also against the following variables: dividend dummy (DD), leverage (LEV), SIZE, return on equity (ROE), future values of ROE, and dummy variables for each sample year (DummyYear), using a fixed-effect panel.The standard errors for the regressors are indicated within parentheses.At the bottom of the Significance levels are displayed in the following manner: *** significant at 1%, ** significant at 5% and * significant at 10%.

Additional Considerations
Pástor and Veronesi (2003) argue that a firm's age is a good proxy for the level of learning by investors, since, according to their model, the variance of investors' expectations of future profitability decreases with time, implying a lower value for the M/B ratio.However, other factors may accelerate or slow down the process of learning about a firm.
The occurrence of relevant changes in a firm's size, for example, as a result of acquisitions and mergers, or large scale changes, may significantly affect the firm's economic fundamentals.In turn, this should increase the investor's uncertainty as to future profitability, reducing the accumulated benefits from learning over time.
Table 5 presents a test of this hypothesis.The percentage change in the firm's total assets for the year (AssetGrowth) was used as an indicator of relevant variations in the firm's size.AssetGrowth was defined as a truncated variable taking on the value of zero if the absolute value of the change in total assets was at most equal to an arbitrary cutoff value, and equal to the actual percentage in total assets if the absolute value was above that level.The cutoff level was chosen to represent the point from which size changes would have a relevant effect on learning by investors.Cutoff levels of 5%, 10%, 15%, 25% and 50% were selected.Table 5 displays the results for AssetGrowth defined with a 50% cutoff level.The results for the other levels were similar to those in Table 5 and are not report for reasons of space.
In order to perform this test, an interaction term involving AGE and Asset-Growth (AGE*AssetGrowth) was inserted into structural model ( 2).This procedure was designed for ascertaining whether the effect of AGE on M/B varied with the level of growth.This implies the following hypothesis for testing purposes: This test was performed with panel data and robust-variance fixed-effect estimators.The results do not lead to the rejection of the null hypothesis.Hence, there is no evidence that the pace of growth diminishes the effect of AGE on M/B.In the Age column, the logarithm of the M/B ratio is initially regressed against the firm's AGE (number of years since initial exchange listing) and the interaction of AGE with asset growth (AGE*Asset Growth).In the remaining columns, as reported also in Table 4, the logarithm of the M/B ratio is regressed against AGE and the interaction of AGE with asset growth, and also against the following variables: dividend dummy (DD), leverage (LEV), SIZE, return on equity (ROE), future values of ROE, and dummy variables for each sample year (DummyYear), using a fixed-effect panel.The standard errors for the regressors are indicated within parentheses.At the bottom of the table, the number of observations and R2 are provided.The reporting of results for the year dummy variables was omitted in order to save space.Age Q=0 Q=1 Q=2 ROE2 0,009 (0,007) N 1773 1772 1548 1333 R2 0,20 0,14 0,11 0,09 Significance levels are displayed in the following manner: *** significant at 1%, ** significant at 5% and * significant at 10%.
One could also consider that the availability of information may have an effect on learning by investors.The greater the availability of information about a firm, everything else constant, the quicker must be the learning process.Hence, the effect of age on M/B would be amplified.In order to test this hypothesis, we have used the existence of American Depositary Receipts (ADR) programs as a proxy for information availability.When issuing ADR's level 2 or 3, the firm must comply with U.S. disclosure rules which are more comprehensive than those prevailing in Brazil, and such information would be available to all investors, including those valuing stocks traded at the BOVESPA.
According to Lameira et al. (2007), in order to have their stock listed at ADRs and traded on U.S. exchanges, firms must enhance their governance practices, both both in informational terms and in terms of "management quality".The former effect could be seen as a substitute or complement for age as an influence on the learning process by investors.
Thus, we define an ADR variable as a dummy variable equal to 1 in the years a firm has ADR's traded, and 0 otherwise.For this test, an interaction term involving ADR and AGE (AGE*ADR) was included in structural model (2).The hypothesis is: Table 6 presents the results of a joint endogeneity test for AGE and ADR.The exogeneity of these variables is not rejected in the fixed-effect regression.Table 7 contains the results of testing for the effect of information availability in the learning process.Once more, the inferences were made with robust variance fixed-effect estimators.The results reject the null hypothesis at the 1% level.The absolute values of the interaction term coefficients are larger than the coefficients for the AGE variable reported in Table 4.This is in agreement with the assumption that the greater availability of information amplifies the effect of AGE on the M/B ratio.This indicates a quicker learning process.However, the coefficient of the AGE variable is not significant in the Q = 1 and Q = 2 regressions, and is significant at 10% in the other specifications.This suggests that the ADR variable should be included in structural model (2).In the Age column, the logarithm of the M/B ratio is initially regressed against the firm's AGE (number of years since initial exchange listing) and the interaction of AGE with the ADR dummy variable (AGE*ADR).In the remaining columns, as reported also in Tables 4  and 5, the logarithm of the M/B ratio is regressed against AGE and the interaction of AGE with ADR, and also against the following variables: dividend dummy (DD), leverage (LEV), SIZE, return on equity (ROE), future values of ROE, and dummy variables for each sample year (DummyYear), using a fixed-effect panel.At the bottom of the Hence, we tested whether AGE continues to be significant after introducing ADR in model ( 2).If ADR is significant, and AGE is not, it must be the case that the learning process takes place more as a function of the availability of information than of the length of time during which the stock has been traded.Table A.1 in the appendix contains the regression results.They are in line with those reported in Table 4, both in terms of their significance and the magnitude of the AGE variable coefficients.The ADR coefficient is non-significant at 5% in all the regressions.
Therefore, the evidence indicates that the combined effect of the length of time during which the stock has been traded and the availability of information is stronger than the sum of the effects of those individual variables.
This contradicts the results in Lameira et al. (2007), who obtain a positive and significant relationship between a firm's value, measured by its market to book ratio, and its participation in an ADR program at any level (1, for over-the-counter trading; 2 or 3, for stock exchange trading), using 2004 data for 64 publicly-traded Brazilian companies.Lameira et al. (2007), however, did not consider the age variable, which could then be seen as an omitted variable in their specification.Leal and Carvalhal-Da-Silva (2005), in a comparative study of the relationship between value and corporate governance quality, using 1998, 2000 and 2002 data for Brazilian and Chilean firms, also found no significant relationship between participation in ADR programs and value (also proxied by market to book ratio).In that study, however, dummies for ADR programs and participation in so-called differentiated governance levels were found to be non-significant, given the inclusion of a governance quality index that already included measures of disclosure quality, such as the requirement that financial statements be prepared and published according to U.S. or international accounting standards.As indicated by Leal and Carvalhal-da-Silva, such variables tend to be redundant, in the presence of other questions they used in their questionnaire, such as that involving statements with the use of international accounting standards.

Conclusions
Return predictability and excess volatility are market-observed anomalies that challenge the market efficiency hypothesis.A possible explanation for such phenomena involves a learning process by investors.Even though investors are rational, they do not know the true distribution of future dividends and improve their parameter estimates over time.This behavior introduces the above-mentioned anomalies, but does not generate arbitrage opportunities.Pástor and Veronesi (2003) developed a model linking learning concepts to stock valuation, and posited the Idea that, the higher the age of a firm in the stock market, the lower its market-to-book ratio (M/B).This would result from the increase in the amount of knowledge accumulated with experience by investors, and, thus from the reduction of uncertainty as to stock values.This implication was tested with U.S. market data and the results did not reject the model implications.
In this paper, a more general methodology was employed in testing for the effect of market age with data for firms listed on the São Paulo Stock Exchange (BOVESPA).Estimation took place with panel data and fixed-effect estimators.The results do not reject the hypothesis that age has a negative effect on M/B, in agreement with the Pástor and Veronesi (2003) results.
In addition, we tested whether the speed of learning by investors, that is, whether the effect of age increases or decreases with the rate at which a firm grows, for instance, through mergers and acquisitions, or with the greater availability of information.The evidence indicates that the greater availability of information amplifies the effect of market age on M/B.Therefore, the evidence for the Brazilian market supports the theory that there is learning by investors, and that the empirical anomalies may result from such a learning process.ROE1

Figure 2
Figure 2Exhibit 2 -Mean and median M/B as a function of age The average of the mean and median M/B values correspond to the average of the M/B ratio for each level of the AGE variable, the latter representing the number of years during which the firm has had its stock listed at the exchange.

Table 2
Correlation coefficient matrix The table provides the correlation coefficients involving market/book ratio (M/B), number of years during which the firm has had its stock listed on the exchange (AGE), dividend dummy variable (DD), leverage (LEV), size (SIZE), return on equity (ROE), future values of ROE (ROE1 and ROE2), dummy variable for ADR (ADR) and AssetGrowth, defined as a truncated variable taking on a value equal to zero if the absolute value of total asset change is at most 50% and equal to the percentage change in total assets if the absolute value

Table 3
Heij et al. (2004)or the AGE variableDurbin-Wu-Hausman endogeneity test and Sargan instrument exogeneity test, as described inHeij et al. (2004).The instruments were defined in regressions of AGE against lagged values of M/B and the other regressors in structural model (2).

Table 4
Fixed-effect regressions table, the number of observations and R2 are provided.The reporting of results for the year dummy variables was omitted in order to save space.

Table 5
Fixed-effect regressions and test for asset growth

Table 6
Heij et al. (2004)or AGE and ADRDurbin-Wu-Hausman endogeneity test and Sargan instrument exogeneity test, as described inHeij et al. (2004).The instruments were defined in regressions of AGE and ADR against lagged values of M/B and the other regressors in structural model (2).

Table 7
Fixed-effect regressions and test for information availability Date of Listing at the exchange List of sample firms, indicating the year in which there stock was first listed at BOVESPA, as well as the source of that information: Economática or research at the BOVESPA Memory Center.Details are provided in section 4.