The Speed of Learning About Firms' Profitability and Their Price Multiples a Global Perspective

7/29/2019 The Speed of Learning About Firms' Profitability and Their Price Multiples a Global Perspective

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The Speed of Learning about a Firms Profitability and its Price Multiple:

A Global Perspective

PANKAJ K. JAIN AND UDOMSAK WONGCHOTI*

______________________

* Jain is from Fogelman College of Business and Economics, The University of Memphis, USA and Wongchoti

is from Massey University, Palmerston North, New Zealand. Please send correspondence to Pankaj Jain, FCBE

425, University of Memphis, Memphis, TN 38152, Phone (901) 678 3810, Fax (901) 678 0839, Email:

[email protected] or [email protected]. We are grateful to Michael Pagano, Ian Cooper, Henk

Berkman, John G Powell, Fei Wu, Ben Jacobsen, and seminar participants at the European Finance Association

Annual Meeting 2008 (Athens, Greece), University of Mississippi, Southern Methodist University, and Old

Dominion Universityfor comments and suggestions. All errors are our responsibility.


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The Speed of Learning about a Firms Profitability and its Price Multiple:

A Global Perspective

Abstract

We present direct global evidence of declining analyst forecast errors, return volatility,

and M/B ratio with progression in a firms age in the context of a learning model

which focuses on the positive numerator effects of uncertainty about the firms

profitability. The convex relation between a firms age and its M/B is pervasive over

time and across countries after controlling for future growth rate, leverage, size,

dividend policy, and future return. Strict enforcement of insider trading laws, higher

feasibility of short selling, and dominance of local versus foreign investors increase

the learning speed and fuel quicker achievement of long run equilibrium valuations.


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Capital markets play an important role in the economic development of any country.

Well functioning markets ensure that both corporations and investors pay or receive fair

prices for their securities. This equilibrium assures that valuable projects are financed and

negative present value projects are rejected. In this framework, valuation of equity securities

involves discounting the profits (dividends, earnings, or cash flows) that a stock brings to the

stockholder in the foreseeable future, and a final value upon disposition.

Much of the financial research, including the seminal CAPM and Fama-French (1992,

1993, and 1995) 3-factor model, is focused on the discount rate and its equity risk premium

component. Formulas for arriving at the profitability of a firm are in place as well. The

calculations, however, depend heavily on accurate forecasts of the firms revenues and

expenses. Accurately forecasting the future demand for a firms products and its future

competitive position is indeed a big challenge. Bulk of the finance literature implicitly

assumes that since the negative errors in forecasting may be offset by an equal amount of

positive errors, such errors may be inconsequential in valuing stocks at the portfolio level.

Only recently, Pastor and Veronesi (2003) suggest that the uncertainty about future

profitability and forecasting errors, even if symmetric around zero, affect asset prices and

valuations because of convexity in the asset pricing formula. The gains from a positive

surprise in growth rate of a firms earnings asymmetrically outweigh the losses from a

negative surprise of the same magnitude. An important and surprising implication of this

model is that the ratio of market value to book value (M/B) declines at a decelerating speed as

a firm ages and investors learn more about the firms expected future profitability and thereby

resolve the associated uncertainty.


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The goal of this study is to enhance our understanding of the learning process and its

valuation implications along several dimensions. First, we establish the validity of the

existence of a learning process and declining uncertainties by directly testing for any changes

in the mean analysts EPS forecasting errors with progression in a firms age. This is an

important link in the learning theory not yet tested explicitly. Second, we present pervasive

global evidence of the valuation implications of the learning theory from firms listed in 52

stock exchanges around the world. Our third contribution deals with a subtle extension of the

concept of speed of learning beyond firm specific characteristics. We do confirm that there

are differences in the learning process for dividend paying and non-dividend paying firms, in

both domestic and international samples. We then extend that logic to demonstrate differences

in the learning process and its valuation implications in economies with diverse market

designs and legal frameworks. In our panel data analysis, the effects of market restructuring

are particularly interesting to analyze because of the near complete transformation of financial

markets in the recent decades (see, e.g., Bekaert and Harvey, 1995; Bekaert and Harvey,

2000; and Henry, 2000, among others). Examples include stricter enforcement of laws

prohibiting insider trading, ever changing regulations on short-selling constraints, and

increased involvement of sophisticated foreign institutional traders in the global markets.

Important empirical questions arise as a result. Does a systematic pattern of learning exist in

all markets? Does the speed of learning change with significant variations in financial market

regulations and foreign investor participation? We develop these hypotheses and provide a

related literature review in section I of the paper.

We then address these issues empirically in a cross-country setting by analyzing a

universe of 22,858 international firms and its various subsets based on data availability from


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DataStream International and I/BE/S International. Data sources and sample characteristics

are shown in section 2. In that section, we also present the results of our data analysis. Both

analyst forecast errors and return volatility decline with progression in an average firms age.

In a multivariate setting, the negative relationship between forecast error and a firms age

remains strong after controlling for other known determinants of analyst errors such as size,

return volatility, debt to asset ratio, and number of analysts. With standardized absolute

analyst forecast errors as the dependent variable, the coefficient of the natural log of a firms

age is 0.013 and statistically significant at the 1% level. This is a direct global evidence of a

learning curve about an average firms profitability among stock market participants.

Consistent with the asset pricing model based on learning, the M/B ratio of the average firm

declines in a convex fashion during its life. The M/B ratio of an average firm in the world is

1.99 in the first year of its appearance in the dataset and it reduces to 1.27 after ten years,

which translates into the cumulative effect of learning on valuation of 0.72 or 72% of its book

value. As a benchmark, a learning effect of 1.00 is reported by Pastor and Veronesi (2003) for

only the NYSE stocks. The valuation effects of learning are pervasive over time and across

countries, and are stronger for firms that do not pay dividends. In a multivariate setting, Pastor

and Veronesi (2003) report the significant relationship between a firms M/B ratio and its age

(defined as minus the reciprocal of one plus firm age to capture non-linear relationship in the

context of learning) as 0.71. This number is economically significant as it indicates the

12.5% valuation difference between an average one year old firm and an average two years

old firm. We report the slightly higher number for the same relationship as 0.81 for a global

portfolio. M/B increases with growth potential and decreases with required equity premium as


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expected. More importantly, the impact of learning on valuation remains strong in the

multivariate regressions after controlling for these other determinants of M/B.

We find that the speed of learning about a firms profitability and its impact on

valuation varies in economies with diverse market designs and legal frameworks and this new

finding advances the prior literature on the subject. The speed of learning or the reduction of

forecast errors with advancement in a firms age is faster with strict enforcement of laws

prohibiting insider trading, higher feasibility of short selling, and dominance of local as

opposed to foreign investors. Our incremental effect analysis reveals that the above conditions

significantly enhance the negative relationship between analysts EPS forecast errors and the

firms age by 0.005, 0.006, and 0.010 per year, respectively. In turn, these features also

fuel quicker achievement of long run equilibrium valuations, especially in the developed

markets. Our results highlight the complex nature of the market environments impact on

rational price discovery process, which is still an on-going debate among academics and

regulators. Our contribution is to shed further light on this important issue from the

perspective of the newly established learning model.

The paper proceeds as follows. In the next section, we formalize our testable

hypotheses. Data and empirical results are provided in section 2. We then conclude and

discuss some potentially fruitful directions for further research in section 3.

1. Testable Hypotheses

H10: The Learning Process:There is a reduction in uncertainty about the profitability of a

firm with advancement in its age:


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0 1

where 2

represents the uncertainty about profitability. Newer firms tend to possess a higher

degree of uncertainty about their product demand, revenue stream, operational cost, cash

flow, and profitability. These uncertainties can manifest themselves in higher analyst forecast

errors in the early years of the firms existence. As time passes by, such uncertainties resolve

because the firm goes through the concrete implementation of its business plans. The analysts

can also forecast the firms profitability more accurately for older firms with more data

availability on actual historic performance and financial results. Markov and Tamayo (2006)

and Linnainmaa and Torous (2009) develop models to explain predictability of analyst

forecast errors based on a learning process, although their focus is on separating learning from

irrationality at the analyst level. We conduct original and direct cross-country tests of

aggregate learning by investigating the relation between median analyst forecast error from

I/B/E/S international and the firms age.

Valuation Model that includes the Numerator Effect of Uncertainty: The learning curve in the

financial markets affects an average firms valuations if the effects of uncertainty are

explicitly modeled. Pastor and Veronesi (2003) predict higher M/B ratios for younger firms

due to greater uncertainty about their future profitability. The genesis of this relationship is

the convexity in the following valuation equation:

])2/exp[(]}){exp[( 2 TrgTrgEB

M+== (2)


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whereM/B stands for market to book ratio, E{.} is the expectations operator, g is the growth

rate, ris the stochastic discount factor, Tcan be interpreted as the time after which the firm is

not expected to grow at an abnormal rate, exp stands for exponential. It is a mathematical

property of this equation that M/B increases in 2

because of the convex relationship between

growth rate and firms stock price valuation resulting from effects of compounding.

Innovation is good and innovative firms are valued highly even when their profitability is

highly uncertain. The absolute wealth increase associated with growth rates one unit above

average dominates the absolute wealth decrease associated with growth rates one unit below

average. With learning, such uncertainties reduce over time.

H20: Valuation Implication of the Learning Curve: Thus, the theoretical prediction about

the effect of learning on valuations is that, ceteris paribus, M/B declines with the

advancement in a firms age:

/

0 /

0 3

Previous literature has confirmed this relationship for U.S. stocks. We present

comprehensive tests of this hypothesis in a global setting.

Speed of Learning: We formulate the concept of speed of learning for a given change

in the learning environment (E) as the change in the rate of reduction of uncertainty in analyst

forecast in each year of a firms life as follows:

4


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The learning environment can be affected by both regulations and the types of

participants present in the market. We focus on two specific regulatory features of a market

and one feature focusing on the investor type. These features are vigorously debated in both

popular press and academic papers and there is no doubt that they affect information and price

discovery process for financial securities. Nevertheless, whether they promote or hinder the

learning process is a matter of great controversy among researchers and regulators. More

importantly, their impact on long term price discovery in the learning context has never been

studied and we intend to fill this gap.

The first learning environment variable in our analysis relates to the laws prohibiting

insider trading. Stricter enforcement of such laws could either slow the learning process or

speed it up depending on the trade-off between internal and external sources of information.

On the one hand such laws eliminate arguably the most informed participants (insiders) from

affecting the knowledge base about a firms profitability. This effect can slow the learning

process. Advocates for this strong form efficiency view include Cornell and Sirri (1992),

Meulbroek (1992), and Chakravarty and McConnell (1997) as they imply that insider trading

results in more rapid price discovery. On the other hand, the persistence of insider trading

puts everyone else at a relative disadvantage; a disincentive for equity research analysts and

expert investors that could generally drive them away from spending efforts towards learning

about any firms profitability. Bhattacharya and Daouk (2002) advocate this research-

expertise view by showing that the cost of equity, an indicator of price efficiency, for a

countrys stock market is lowered when insider trading laws are enforced effectively through

actual prosecutions. Empirical analysis is necessary to determine which of these two effects

dominate in our learning context. We divide the firm-years into those before and those after


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the first enforcement of insider trading law in each country. The cut-off year for each country

is taken from Bhattacharya and Daouk (2002).1

The second aspect of the learning environment is the feasibility of short-selling stocks

without owning them. Here again there is a predatory short selling view versus a complete

markets view. Predatory short selling interferes with the learning process through price

manipulation and this view is proposed in the literature summarized by Shkilko, Van Ness,

and Van Ness (2008). In contrast, according to the complete markets view, the ability to

short-sell could be an important tool towards rational price discovery as it allows arbitrageurs

or analysts to exploit both positive and negative news about a firm. Without this tool, there

are limited incentives to search for negative information about stocks that one does not own.

This bias can lead to inefficient price discovery since some information (especially negative

information) is not fully incorporated into prices. The effect of short sales constraints on the

speed of price adjustment to private information is modeled in the classic work of Diamond

and Verrecchia (1987). Recent empirical works are consistent with the view that short-selling

activities promote price discovery. Based on a study on 46 equity markets, Bris, Goetzmann,

and Zhu (2007) provide the evidence that negative information is incorporated into prices

faster when short selling is feasible and practiced. Charoenrook and Daouk (2005) also find

that cost of capital is lower and liquidity is higher in countries where short selling is feasible.

As a result, we conjecture that the feasibility of short-selling helps sharpen the learning

process. We divide the sample into markets where short selling is feasible versus those where

it is infeasible. This information is obtained from Charoenrook and Daouk (2005). They study

the impact of short selling constraints on the cost of equity (the discounting rate in asset

1 The article provides both the dates of enactment and first enforcement of law and recommends that the latter

date is more meaningful.


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pricing models, which is a denominator effect) whereas we focus on reduction in uncertainty

of the cash flows through learning (a numerator effect). Short selling facility is likely to

enhance the learning process by rewarding both positive and negative findings about the

prospects of a stock.

The third aspect of learning environment that we analyze is the intensity of

involvement of foreign institutional traders in a countrys stock markets. A rich literature has

emphasized and tested differences between local and foreign investors in terms of their

information seeking and processing behavior for stock trading. Mixed findings have emerged

from those studies. On the one hand, foreign investors can speed up the learning process

because they can bring more sophisticated research skills into the country. Studies which

show that foreign investors are equipped with better information include Grinblatt and

Keloharju (2000), Seaholes (2000), Froot, OConnell, and Seaholes (2001), and Froot and

Ramadorai (2000). However, one can also view the involvement of foreign institutions as

being associated with factors that can introduce a lot of noise in the valuation process and

slow down the learning process. Such factors include capital flight, language barriers, and

deviation of systemic or idiosyncratic foreign factors from domestic factors. Moreover, recent

empirical evidence is pointing to the informational advantage possessed by local investors in

studies that provide a rational justification for home bias (see, e.g., Hau, 2001; Choe, Kho,

and Stulz, 2005; Dvorak, 2005; Bae, Stulz, and Tan, 2008, among others). We believe that

further empirical investigation focusing directly on the analyst forecast errors and valuation

ratios can help us understand whether foreign institutions add more speed or more noise to the

learning process. Thus, we collect information on the extent of foreign investor involvement

in various stock markets. Of the 52 countries in our sample, only 40 countries have foreign


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institutional trading data available in the Plexus database.2

Thus, a reduced sample is analyzed

for this set of regressions. We divide the total dollar volume of all trades undertaken by

foreign institutions in a country by the total market capitalization of that countrys stock

market. Based on the median of this measure we partition the sample into countries with high

versus low foreign institution involvement.

These above arguments lead us to our next hypothesis about the speed of learning.

Against the null hypothesis of no effect of learning environment features, we test the

following alternative hypothesis by comparing the rate of decrease in analyst forecast errors

over time, across markets with opposite learning environment features.

H30: Learning Environment: Various aspects of the learning environment affect the

investors speed of learning and thus the stocks long run equilibrium valuations.

0

/

0 5

We test this hypothesis separately for each aspect of the learning environment. For

example, the tests for the effect of short selling compare the rate of decrease in analyst errors

over time in markets with feasible short selling against the rate of decrease in markets with

restricted short selling. Analogously, we partition the sample along the other two dimensions

of the learning environment.

2. Data and Empirical results

Our main data sources are I/B/E/S International and DataStream International. We

obtain data item forecast period (FPEDATS), stock ticker symbol (TICKER), mean analyst

2 The details of Plexus dataset are described in Chiyachantana et al. (2004).


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forecasted EPS (MEANEST), number of analysts or forecasters (NUMEST) for each stock for

each fiscal year end, and actual EPS (data ACTUAL) from I/B/E/S summary file for each of

the 12,453 US firms and the 21,271 international firms during each available fiscal year and

then focus on the period from 1981 to 2004. We obtain market to book ratio (data item

mnemonic MTBV), dividend per share (DPS), total assets (DWTA), return on equity

(DWRE), long term debt (account item 321), stock return index (RI), and stock price (P) for

22,858 international firms from DataStream International. We verify the accuracy of this

historical data by comparing it with Compustat Global datasets and Yahoo Finance for one

company in each country. The next important item we need is the age of each firm. Direct

information on this variable is not available in any traditional dataset. Therefore, we follow

Fama and French (2001) and Pastor and Veronesi (2003) and use the year of first appearance

of a firms stock price in the dataset as its year of birth.3

Subsequently, we increment age by 1

year in each calendar year.

A. Evidence of learning process in a univariate setting

Table 1 provides preliminary evidence consistent with Hypothesis 1 along two

dimensions. First, we investigate whether there is a long-run declining trend of analyst

forecast errors with progression in a firms age. Analyst forecast error is computed as the

absolute difference between mean analyst forecast and actual year-end EPS, divided by the

absolute actual year-end EPS. Panel A shows that median analyst forecast error is 20.69% for

3 We start this process from the year 1969 which is the first year of availability of price data in DataStream. Oursample ends in the year 2004 implying that the maximum age that any firm can attain in our sample is 36 years.

We realize that the one-year old 1969 firms are actually older in age but such firms do not dominate our dataset.

Our results are also robust when we exclude them and rerun the analysis for various sub-samples.


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1 year old US firms and 11.42% for 20 year old US firms.4

The difference of 9.27% between

the two median errors is statistically significant at 1% level and can be interpreted as the

cumulative amount of learning. This finding verifies an important but untested assumption

implicit in the Pastor and Veronesi (2003) learning model which states that investors learn

about a firms profitability with advancement in its age. In Panel B, we establish that the

learning process is omnipresent in the worldwide sample of firms. The cumulative magnitude

of learning of 9.08% in the international sample is very similar to the US sample, although

international firms within any given age group have larger errors than the US firms in the

same age group. In unreported results, we also verify that analyst forecasting errors are larger

for younger firms than for older firms, whether we use raw analyst errors or errors scaled by

stock price, or just as they are for errors scaled by absolute EPS.5

[Insert Table 1 about here]

Another dimension of uncertainty about the firms profitability is its return volatility.

We compute return volatility as the standard deviation of monthly returns for each stock-year.

Panel C of Table 1 shows that return volatility declines with progression in a firms age.

Median return volatility is 11.89% for 1 year old firms and 7.75% for 20 year old firms. The

difference between the two groups is 4.13%, which is statistically significant at the 1% level.

B.Country-wise analysis of the impact of the learning process on a firms price multiple

4 The forecast errors are low in the IPO year of the firms, jump up in year 2 and then decline monotonically

making the error plot hump-shaped. Reasons for low errors in the IPO year could include the notion that costs in

the project build-up stage (when there are usually no revenues) could be easier to forecast than the combination

of revenues and costs in the subsequent years. The legal consequence of erroneous predictions in the IPOprospectus is also more severe than the analyst forecast errors in subsequent errors.5 For example, stock price-scaled analyst errors average 6.54% for 1 year old firms, 4.77% for 10 year old firms,

and 3.21% for 20 year old firms.


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The value implication of the learning process is that M/B ratio declines with

progression in a firms age, as stated in our second hypothesis. Table 2 presents the median

M/B ratio in 52 countries for firms with ages ranging from one to 10 ten years. Ratios for US

firms, shown in bold font, are reproduced from the Pastor and Veronesi (2003) article. Our

international evidence is consistent with the patterns found in their study and serve to

establish the pervasive global application of their learning model. For the overall sample,

median M/B of 1 year old firms is 1.99 compared to M/B of 1.27 for 10 year old firms. The

difference of 0.72 between the two groups reported in the second last column is statistically

significant at the 1% level. We present country-wise results for each of the 52 countries. The

countries are grouped into developed and emerging markets based on the classification

obtained from Morgan Stanley Capital Internationals website at mscidata.com. The direction

of the change in M/B is consistent with the learning model in 46 out of the 52 countries or

88% of our sample and the difference is statistically significant in 43 countries or 83% of the

sample countries. The countries with some of the biggest learning effects include Netherlands,

Japan, and France among the developed markets and Egypt, Thailand, and Morocco among

the emerging markets. We corroborate these country-wise findings on the valuation

implications of the learning process in multivariate settings in the following sections.


C. Multivariate analysis of the valuation implications of the learning model

Now we perform an international panel data regression to confirm the significance of

the inverse relationship between M/B and firms age, controlling for other factors that are

known to affect M/B6:

6 For all regression analyses, except M/B regressions, we winsorize observations with any variable at the 1st and

99th percentile, to arrive at the final sample. Following Pastor and Veronesi (2003), only M/B ratios in the range


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log(M/B)i,t = a + b.AGEi,t + c.DDi,t + d.LEVi,t + e.SIZEi,t + f.ROEi,t + g.ROE(1)i,t

+ h.ROE(2)i,t + i.ROE(3)i,t + j.RET(1)i,t + k.RET(2)i,t + l.RET(3)i,t++ i,t (6)

where i = 1- N, N being the number of firms in each year t. AGE is defined as - 1/ (1+ Firms

Age) as this specification captures the convexity in the relationship between a firms M/B and

its age in accordance with Pastor and Veronesis (2003) learning model. DD is the dividend

dummy with value 1 for dividend paying firms and 0 for non-payers. LEV is the debt to asset

ratio. SIZE is the natural log of the firms total asset. Pastor and Veronesi (2003) utilize the

Bayesian updating technique in their learning model to predict the relationship between M/B

and expected profitability to be positive and that between M/B and expected future stock

returns to be negative. In our regression, ROE is the return on equity. Explanatory variables

include three leading years terms of ROE for the M/B in year t. RET is future annual stock

return up to three years from current period. The standard errors are clustered by firms to take

into account residual dependence created by firm effect, as suggested by Petersen (2009).7

The results are shown in Table 3.


The global prevalence of inverse relationship between a firms M/B ratio and its age,

as implied by the learning model, is confirmed in the regression framework where the

coefficient on age is -0.81 with a t-statistics of -17.22, which makes it highly significant at the

1% level. The magnitude of the coefficient compares well with the benchmark for NYSE

of 0.01 to 100 are included in the sample. Firms which were born in the year 2002 onwards are also excludedfrom regressions as we need three years of data for future ROE and annual stock returns.7 In line with Pastor and Veronesi (2003), we also verify in unreported results that Fama and Macbeth (1973)

style regressions lead to the same conclusions as clustered standard errors method reported in the Tables.


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stocks during 1962 to 2000 analyzed by Pastor and Veronesi (2003). They report an AGE

coefficient of -0.71 which translates into an economically significant 12.5 percent difference

in valuation between one year old firms and two years old firms. The coefficients on control

variables are in the expected direction. There is a positive relation between future growth in

profitability and the M/B ratio implying that investors pay a higher price for firms with higher

growth prospects (g). Future stock returns are negatively correlated with the M/B ratio on the

measurement date implying that investors are willing to accept a lower equity premium (r) by

paying a higher stock price today for the high M/B stocks. It is important to note that the

effect of uncertainty about profitability (

2

), measured through a firms age, survives in these

regressions after controlling for these other important determinants of M/B ratio.

We divide this sample as well into developed and emerging markets. The coefficient

on age is more negative in the emerging markets. One interpretation of this finding is that the

lower quality of disclosures in emerging markets increases the uncertainties about the cash

flows of the new companies. Therefore, investors have to learn more from the companys

actual cash flows than from the financial projections. The other interesting insight includes a

stronger preference for dividend payments in emerging markets. M/B ratio is 0.14 times

higher for dividend payers in emerging market relative to non-payers. This preference might

be a reflection of the severity of free cash flow problems in the emerging markets, where poor

regulations might make it easier for the corporate management to steal retained earnings from

the shareholders by siphoning it away. On the contrary, M/B ratio is lower by 0.16 times for

dividend payers in developed markets, relative to non- payers in those markets, where growth

effects of earnings retention might dominate the free cash flow problem because of stronger


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shareholder rights. Results in all panels of Table 3 are consistent with our second hypothesis

which states that the learning process affects valuations.

D. Learning process for dividend payers versus earning retainers

We now further explore the direct effects of dividend policy on the learning process

by interacting dividend payment status with firm age. Dividend payments have two potential

effects on the M/B ratio in the context of learning. One effect of dividend payments is a

quicker reduction in the uncertainty about the cash flows that investors receive from younger

firms. A bird in hand is better than two in the bush. The company can lose undistributed

profits in the future but it cannot reclaim distributed dividends because of the limited liability

feature. Moreover, managers tend to smooth dividend payments over time. Thus, dividend

policy can release information to the outside investors about managements expectations of

future profitability. Another effect of dividend payments in the context of learning is that

dividends can reduce the firms reinvestments and growth rate and the corresponding

uncertainty about growth (Pastor and Veronesi (2003)). Both of these effects reduce the

convexity of the relationship between a firms M/B and its age. We examine this issue in the

global context in Table 4.


Results in Table 4 are based on an extended version of the regression equation (6)

presented earlier. To capture the incremental effect of dividend payments on the learning

process, we now have an interaction term between AGE and the dividend dummy, in addition

to the other variables discussed previously. We find that a firms dividend policy plays an

important role in determining the strength of the relationship between the firms M/B and its


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age. In the overall sample and in the developed markets, the interactive variable has a

statistically significant positive coefficient. This implies that dividend payments weaken the

convexity of the relation between M/B and age in the global markets, consistent with Pastor

and Veronesi (2003) prediction of lower growth rate and growth uncertainty of dividend

paying firms.The coefficient on the interaction term of age times dividend dummy is positive

0.56 and statistically significant in Panel A for the entire sample and 0.60 and statistically

significant in Panel B for the developed markets. In emerging markets, the interaction term

has a coefficient of 0.079, which is positive but statistically insignificant with a t-statistics of

0.43.It is possible that the overall uncertainty in the emerging markets is so high that learning

effects of dividends are not sufficiently large to attain statistical significance.

E. Effects of learning environment features on analyst forecast errors

We now merge the firm-specific and country-specific information from the various

data sources i.e. I/B/E/S, DataStream International, and proprietary or hand-collected time

series database on the learning environment values for each country. The purpose of this

exercise is to understand the incremental effects of each learning environment variable. How

does a change in a given feature of the learning environment affect the learning process of

analysts and investors and the valuation of a firms stock? The final sample for this analysis is

the subset of firm-year observations obtained by the triangular intersection of the three data

sources mentioned above.

First, we test whether the mean analyst forecast error is significantly related to a firms

age after controlling for other known determinants of analyst errors in EPS forecasting. Table

5 presents several variations of regression results all of which point to an inverse relationship


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between analyst errors and the firms age. For each firm-year observation, the dependent

variable is the price-scaled absolute analyst forecast error. The first row uses only the firms

age as the explanatory variable; the second row adds control variables commonly used in

analyst forecast literature such as Thomas (2002) in the list of explanatory variables; and the

third row adds control variables from the Pastor and Veronesi (2003) learning model. Results

in Panel A are based on all countries. Results for sub-samples based on developed markets are

in Panel B, emerging markets in Panel C, and just the U.S. in Panel D. The coefficient on

age is negative and statistically significant in each Panel. This finding is consistent with the

learning process stated in our first hypothesis. The coefficients on the control variables are

generally consistent with prior literature and can be interpreted as follows: firm size matters;

the bigger the firm, the smaller are the errors. Consistent with previous studies, analyst

forecast errors decline with the number of analysts, whereas they increase with leverage and

return volatility. With all these control variables included in the regression, the negative

relationship between analyst forecast errors and the firms age remains significant at the 1%

level. Our findings represent the first large scale worldwide evidence of the existence of a

learning curve for the equity analysts of an average firm.


Next, we turn our attention to three different features of the learning environment in

each country to analyze how they affect the learning process. These features are: the history

of actual enforcement of laws prohibiting insider trading as indicated by a history of actual

convictions, the feasibility of executing short sales by investors who possess negative

information but do not own the stock, and the above median involvement of sophisticated

foreign institutional traders in a country. For each feature, we define a learning environment


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20

indicator dummy variable (E) and assign it the value of 1 for the country-years when that

feature is present and 0 if it is absent.

We find a rich cross-sectional variation as well as time-series variation in the learning

environment features across countries. At the beginning of our sample in 1981, the proportion

of firms from countries where prohibition against insider trading was enforced is 11% and this

proportion increases to 84% by 2004. The proportion of firms from countries where short

selling is feasible changes from 96% in 1981 to 72% in 2004. Although this statistic might

seem odd, it is a manifestation of typical regulatory responses to major market crashes. Thus,

not many countries thought about restricting short sales until the 1987 crash, when a host of

restrictions were considered by the regulators. Many restrictions are typically removed once a

significant amount of time has elapsed after a major crash. Thus, short selling feasibility has a

tremendous amount of cross sectional and time series variation in our sample. Finally, the

proportion of firms-years where foreign institutional holding is above median is constant at

50% for each year by definition.

We now re-estimate the analyst forecast error regressions similar to Table 5, but only

after adding the interactive learning environment * age variables among the explanatory

variables and we report the results in Table 6. Separate regressions are estimated to assess the

effect of each learning environment variable. A negative coefficient should be interpreted as

faster speed of learning.


Enforcement of insider trading laws speeds up the rate of decline of analyst forecast

errors with progression in a firms age. Thus, the incentives for outside analysts to generate

profitable information through independent research outweigh any information losses from


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21

disallowing corporate insiders from interfering with the price discovery process. Regulators

should, therefore, enact insider trading prohibitions and enthusiastically prosecute insider

trading cases to improve the learning environment in the financial markets. Feasibility of

executing short selling transactions is another market environment feature that speeds up the

rate of decline of analyst forecast errors with progression in a firms age. This finding is

consistent with our hypothesis that short selling creates bigger incentives for learning about

both positive and negative information about a firms profitability. Opposite results are

obtained for the third feature of learning environment. The involvement of foreign

institutional investors appears to generate higher errors for older firms, which is inconsistent

with the notion of a learning curve. Thus, it appears that the noise introduced by factors such

as capital flight, language barriers, or deviation of systemic or idiosyncratic foreign factors

from domestic factors outweigh the sophistication and skill that foreign investors might bring

to a stock research in a given country. Collectively, our results are consistent with the view

that enforcement of laws prohibiting insider trading laws, short-selling feasibility, and

dominance of local investors are associated with a better learning environment and reduced

uncertainty about a firms profitability.

F. Valuation implications of the learning environment and the speed of learning

Finally, we estimate an incremental effect regression model similar to one proposed by

He and Ng (1998) to investigate the incremental effect of learning environments on learning

speed, which is captured by the negative and convex relationship between delta M/B, i.e., the

rate of change in M/B ratio (or log(M/B)t - log(M/B)t-1), and the firms age :

DELTA M/B = cd0E + cd1E.AGEi + cd2E.DIVi + cd3E.LEVi + cd4E.SIZEi + cd5E.ROEi+ cd6E.ROE(1)i + cd7E.ROE(2)i + cd8E.ROE(3)i + cd9E.RET(1)i


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22

+ cd10E.RET(2)i + cd11E.RET(3)i + c0 + c1AGEi + c2DDi + c3LEVi

+ c4SIZEi + c5ROEi + c6ROE(1)i + c7ROE(2)i + c8ROE(3)i+ c9RET(1)i + c10RET(2)i + c11RET(3)i + i (7)

where (i = 1- N, N is the # of firms). AGE is defined as - 1/ (1+ Firms Age), which captures

the convex relationship between M/B and firm age in the Pastor and Veronesi (2003) learning

model. DIV is the dividend dummy with value 1 for dividend paying firm and 0 otherwise.

LEV is the debt to asset ratio. SIZE is the natural log of the firms total assets. ROE is the

return on equity. Explanatory variables include three leading years terms of ROE for the M/B

in year t. RET is future annual stock return up to three years from current period.Erepresents

learning environment dummy variable. E equals 1 when the particular learning environment

feature is present and 0 otherwise, as described in the previous section. To capture the

incremental effect of the learning environment, we interact all of the base variables with the

environment dummy. All variables of firms in each country are measured in its own currency.

There are 9,640 firms (68,034 firm-year observations) with valid data for all variables in the

final sample. Of these 6,631 firms are from developed markets and 3,009 firms are from

emerging markets. All t-statistics reported in parentheses are based on clustered standard

errors as suggested by Petersen (2009). For brevity, we report only three regression

coefficients, AGE,E, and AGE*Ein Table 7. Panel A is based on a full dataset whereas Panel

B and Panel C are based on developed market and emerging market sub-samples,

respectively. Three separate regressions are reported in each panel, one for each learning

environment.


The negative coefficient on AGE variable in every panel establishes the inverse and

convex relation between a firms M/B and its age. The second column is simply the direct


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23

effect of a given feature of the market on the firms valuation. Note that the coefficients in

this second column only capture the level of valuations and are not related to the learning

model because the learning model requires an interaction of the learning environment

variables with the firms age. From the overall sample used in Panel A, we observe that all

three market features have positive coefficients. Thus, we conclude that enforcement of

insider trading laws, feasibility of short selling transaction, and increased presence of foreign

institutional investors are all associated with higher stock valuations. Thus in the valuation

sense, these features are good. However, to assess the impact of these features on the speed of

learning and change in M/B, we interact the firms age with the learning environment

dummies. The coefficients are in the third column. Negative coefficients represent faster

speed according to the learning model. There is a negative coefficient on enforcement of

insider trading which suggests that this feature speeds up the learning process. In contrast,

positive coefficients on short selling and foreign investors suggest that those features actually

slow the learning process. In Panel B for developed markets and Panel C for emerging

markets, we see that the results are consistent with the overall results for speedier learning

with enforcement of insider trading and slower learning with above median foreign

institutional investors. However, the short selling activities have opposite effects in developed

versus emerging markets. Short selling appears to speed up the learning process only in

developed markets. In emerging markets short selling is slowing the learning process through

additional noise. The overall conclusion from the table is consistent with our third hypothesis

which states that various features of learning environment matter as determinants of the speed

of learning.


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G. Robustness tests

We conduct several robustness checks to establish the reliability of our results and

investigate the extent to which our findings can be generalized. Robustness tables are not

included in the manuscript for brevity but will be available from the authors or from the data

section of the journal website, if this facility is provided. Earlier in Tables 1 and 2, we showed

that the decline in analyst forecast errors and M/B ratio with the advancement in the firms

age is pervasive across markets and countries. As the first robustness test, we divide our

sample into various sub-samples focusing on the time-period dimension. Average M/B for 1

year old firms is significantly higher than the average M/B for 10 year old firms in both 1981-

1992 and 1993-2004 sub-samples. Similar result is obtained in three sub-samples which are

formed before the internet bubble, during the internet bubble period of 1990 to 1999, and after

the bust of the bubble.

All of our main conclusions are based on heteroskedasticty consistent White standard

errors; they are also robust to alternative regression techniques such as country and year fixed

effects, Fama-Macbeth style regressions, and clustered standard errors suggested by Peterson

(2009).

Although most of our analysis is theoretically unaffected by currency exchange rates

because scaled analyst errors or valuation ratios do not have any currency units, we verify that

the results are in the same direction when we use dollar denominated variables as input as

they are when we use local currency denominated variables. Similarly, we rerun the

regressions with alternative scaling parameters. For example, price scaled analyst error are

used as dependent variables for regressions reported in Tables 5 and 6. When we use analyst

errors scaled by absolute EPS, the coefficient for age remains negative and statistically


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25

significant. Similarly, the coefficients are negative and significant for the interactive variables

where a firms age is interacted with the three learning environment features, i.e., age times

stricter enforcement of insider trading prohibitions, age times feasibility of short selling, and

age times dominance of local over foreign investors. Thus, our conclusions about the

usefulness of these learning environment features are robust to alternative ways of scaling

analyst forecast errors.

We also consider several additional control variables in the regression analysis. The

main variables with consistent data availability represent market design and industrial sectors.

For automated market design, we use the fully computerized trading system as the proxy. Our

prior is that advanced trading technology could speed up the learning process. For industrial

sectors, we use NAICS classifications to form a dummy indicator variable of traded versus

non-traded industries. Here our prior is that, in a global setting, investors could learn faster

about profitability of firms dealing in traded goods using profitability experiences from

similar firms elsewhere as well as from futures price information available in global

commodity markets. However, the empirical results demonstrate that these additional

variables do not add any explanatory variables to the regressions. More importantly, the

inverse and convex relation between a firms M/B and its age as well as the inverse relation

between analyst forecast error and the firms age remain significant after including these

variables.

3. Conclusion

This paper provides ubiquitous evidence consistent with an intriguing valuation theory

that takes into account a learning curve among stock market analysts and investors. The


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valuation model proposed by Pastor and Veronesi (2003) assumes that investors face

significant uncertainty about profitability and cash flows of young firms. Unlike the

traditional focus of asset pricing models on the denominator or discount rates, they focus on

how the uncertainty affects the expected value of cash flows in the numerator. The convex

nature of the valuation equation implies that uncertainty actually increases a new firms M/B.

However, as time passes, investors learn about the true potential of a firms profitability and

resolve the uncertainty. Thus, the model predicts that M/B is higher for younger firms than for

older firms.

In this paper, we provide a comprehensive empirical analysis of this issue in a global

setting. By directly showing that analyst forecast errors decline with advancements in a firms

age, we provide an important link in the learning theory not yet tested globally in the

empirical literature. Return volatility of stocks in global, developed, and emerging markets

also decreases with the firms age. Next, we present pervasive international evidence of the

valuation implications of the learning theory from firms listed in 52 stock exchanges around

the world. Over eighty percent of the countries have statistically significant valuation changes

consistent with the learning theory. This inverse and convex relationship between a firms

M/B and its age is economically and statistically significant in the regression framework after

controlling for other factors known to determine the market-to-book ratio such as future

growth potential and expected equity premium. The inverse relationship between a firms

M/B and its age is also more striking for non-dividend paying firms.

We extend the concept of speed of learning beyond firm-specific characteristics. Our

goal is to understand the impact of diverse market designs and legal frameworks on the

learning process. The three key learning environment features included in our analysis are


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27

stricter enforcement of laws prohibiting insider trading, feasibility of short-selling, and an

increased involvement of sophisticated foreign institutional traders in the firms primary stock

market. Enforcement of laws prohibiting insider trading speeds up the rate of decline of

analyst forecast errors with progression in a firms age, and consequently firms are valued at

their long run equilibrium values more quickly. Thus, the incentives for outside analysts to

generate profitable information through research outweigh any information losses from

disallowing corporate insiders from interfering with the price discovery process. Regulators

should, therefore, enact insider trading prohibitions and enthusiastically prosecute insider

trading cases to improve the learning environment in the financial markets. Feasibility of

executing short sell transactions is another market environment feature that speeds up the rate

of decline of analyst forecast errors with the progression in a firms age. This finding is

consistent with our hypothesis that short selling creates bigger incentives for learning about

both positive and negative information about a firms profitability. However, despite lower

analyst errors in all markets, the short selling activities have opposite valuation effects in

developed versus emerging markets. One potential interpretation of this finding is that

predatory short selling might introduce more noise in emerging markets and outweigh the

uncertainty resolution effects of research. Finally, the involvement of foreign institutional

investors appears to generate higher errors for older firms, which is inconsistent with the

notion of sophisticated foreign investors enhancing the speed of learning. Thus, it appears that

the noise introduced by factors such as capital flight, language barriers, or deviation of

systemic or idiosyncratic foreign factors from domestic factors outweigh the sophistication

and skill that foreign investors might bring to equity research environment in a given country.


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When domestic investors dominate, learning speed is faster and consequently M/B valuation

ratio approaches long term equilibrium faster.

Future research can explore additional determinants of the speed of learning and also

develop more advanced theoretical constructs for this concept. The results in this paper

implore that asset pricing models include the learning curve as an important factor. The

learning process about a firms profitability has important implications for stock valuation all

around the world.


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29

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Table 1

The Learning process: Declining uncertainty with advancement in a firms age

Panel A. Declining Analyst Forecast Errors for US Firms

Firms Age in Years 1 2 3 4 5 6 7 8

Forecast Error 20.69% 29.27% 31.56% 31.79% 30.77% 27.45% 23.99% 25.00%


Forecast Error 19.40% 19.12% 18.58% 17.32% 15.75% 16.34% 15.69% 13.63%

Total Learning 9.27%***

Panel B: Global Evidence on Declining Analyst Forecast Errors


Forecast Error 23.08% 31.92% 33.33% 33.56% 34.49% 32.26% 30.83% 30.79%


Forecast Error 23.19% 23.57% 24.64% 24.14% 22.05% 24.73% 23.19% 18.88%

Total Learning 9.08%***

Panel C: Declining Return Volatility for Firms around the World


Return Volatility 11.89% 11.32% 11.28% 11.19% 10.75% 10.64% 10.29% 9.95%


Return Volatility 10.02% 9.89% 9.17% 9.74% 9.38% 8.59% 8.38% 9.03%

Total Reduction 4.13%***

We obtain mean analyst forecasted EPS and actual EPS from I/B/E/S international dataset from 1981 to 2004. Analyst for

as the absolute difference between mean forecasted EPS and actual EPS, divided by the absolute actual EPS. Data are winand 99th percentile to eliminate potential outliers and data input errors. The first appearance of a firm in the database is

firms year of birth. Each year, firms of the same age are grouped together. Panel A uses only 12,453 US firms and shforecast errors for firms within each age group. Panel B repeats the analysis including 21,271 international firms. Next,

return for each firm from Datastream International. Return volatility is computed as the standard deviation of monthly retu

year of observation. Panel C presents the median return volatility for firms within each age group. Total learning is the diand year 20. Asterisks indicate statistical significance at the 1% level with ***.


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Table 2

Country-wise analysis of the impact of the learning process on firms price multiples

Age 1 2 3 4 5 6 7 8 9 10

Cumu

effect

learni

valuat

All firms 1.99 1.79 1.62 1.55 1.43 1.43 1.41 1.37 1.30 1.27 0

Panel A: Developed markets

Australia 1.68 1.55 1.38 1.40 1.20 1.48 1.43 1.56 1.36 1.33 0

Austria 1.49 1.31 1.12 1.23 1.30 1.27 0.98 1.03 0.98 0.97 0

Belgium 1.62 1.30 1.18 1.24 1.15 1.18 1.05 1.18 0.97 1.03 0

Canada 1.54 1.56 1.49 1.55 1.50 1.50 1.61 1.71 1.60 1.56 -0Denmark 1.22 1.28 1.07 1.13 0.99 1.14 1.08 1.01 0.96 0.99 0

Finland 1.50 1.23 1.22 1.31 1.35 1.33 1.3 1.22 1.22 1.39 0

France 2.29 1.90 1.60 1.40 1.40 1.30 1.19 1.09 1.16 1.23

Germany 2.37 1.95 1.55 1.32 1.33 1.69 1.90 2.10 2.11 1.86 0

Hong Kong 1.71 1.40 1.20 1.08 0.90 0.87 0.87 0.75 0.81 0.81 0

Ireland 1.81 1.71 1.55 1.61 1.59 1.64 1.58 1.87 1.79 1.88 -0

Italy 1.60 1.51 1.40 1.39 1.15 1.05 0.94 0.99 1.00 0.91 0

Japan 2.42 2.27 1.98 1.79 1.53 1.48 1.54 1.40 1.37 1.17

Luxemboug 0.87 1.40 1.26 1.19 1.44 1.88 1.81 1.34 1.05 0.90 -0

Netherlands 2.63 2.46 2.01 1.795 1.74 1.53 1.77 1.73 1.28 1.12


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Table 2 ..Continued.

Age1 2 3 4 5 6 7 8 9 10

New Zealand 1.36 1.22 1.07 1.02 1.02 1.03 1.04 1.31 1.35 1.30 0Norway 1.50 1.30 1.30 1.26 1.32 1.31 1.28 1.29 1.38 1.25 0Portugal 1.84 1.76 1.63 1.51 1.35 1.30 1.28 1.00 1.09 1.20 0Singapore 2.02 2.01 1.72 1.80 1.71 1.36 1.52 1.42 1.44 1.30 0Spain 1.83 1.66 1.55 1.30 1.37 1.30 1.43 1.41 1.48 1.66 0Sweden 2.07 1.99 1.90 1.70 1.45 1.55 1.59 1.55 1.49 1.61 0

Switzerland 1.50 1.31 1.17 1.19 1.11 1.07 1.16 1.11 1.11 1.04 0

UK 2.61 2.22 1.97 1.83 1.79 1.75 1.70 1.68 1.66 1.76 0

USA 2.25 1.80 1.57 1.49 1.39 1.38 1.35 1.33 1.27 1.25 1

Panel B: Emerging markets

Argentina 1.22 1.00 1.04 1.34 1.19 0.84 0.78 0.58 0.4 0.65 0.

Brazil 0.83 1.28 0.82 0.75 0.92 0.97 0.95 0.93 0.66 0.585 0.

Chile 1.18 1.12 1.63 1.43 1.28 1.44 1.33 1.08 0.97 0.74 0.

China 3.33 2.70 2.50 2.75 2.76 2.56 2.58 3.10 3.31 3.01 0.

Colombia 1.09 0.72 0.74 0.65 0.43 0.53 0.56 0.51 0.48 0.545 0.

Czech Rep. 0.77 1.20 1.01 0.66 0.74 0.5 0.45 0.54 0.82 0.42 0.

Egypt 2.34 2.87 1.63 1.6 1.27 0.93 0.82 1.04 0.5 0.34 2.

Ethiopia 2.5 1.47 2.1 2.78 2.85 2.5 1.47 2.1 2.14 2.99 -0.

Greece 2.53 2.23 1.89 1.91 1.42 1.53 1.35 1.25 1.22 1.98 0.

Hungary 1.49 1.06 1.20 1.10 0.96 0.9 0.94 0.94 0.78 0.74 0.

India 1.84 1.85 2.01 2.16 2.12 2.23 1.54 1.34 1.04 0.89 0.


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Table 2 ..Continued.

Age1 2 3 4 5 6 7 8 9 10

C

ef

Indonesia 1.69 1.28 1.18 1.25 0.93 0.88 0.83 0.79 0.75 1.15 0.

Israel 1.94 1.84 2.31 1.86 1.51 1.16 1.54 1.92 1.61 1.83 0Korea 1.45 1.26 1.06 0.87 0.83 0.91 0.78 0.69 0.61 0.66 0.

Malaysia 1.47 1.44 1.42 1.50 1.28 1.17 1.12 1.29 1.41 1.40 0

Mexico 1.23 1.49 1.25 1.19 1.13 1.19 1.11 0.97 1.06 1.00 0.

Morocco 2.98 2.07 2.40 2.01 2.03 2.31 2.10 1.74 1.62 1.48 1.

Pakistan 1.81 2.61 1.96 1.18 0.93 1.00 0.78 0.83 1.01 0.92 0.

Peru 1.31 1.08 1.18 1.10 1.06 0.95 0.84 0.81 0.75 0.77 0.

Philippines 1.86 1.75 1.39 1.21 1.29 1.24 1.14 1.02 0.81 0.8 1.

Poland 1.13 1.10 1.12 1.20 1.12 1.33 1.28 1.31 1.04 1.00 0.

Russia 0.39 0.30 0.62 0.31 0.43 0.37 0.36 0.30 0.65 0.19 0.

South Africa 2.31 2.22 1.61 1.19 1.25 1.32 1.25 1.44 1.03 1.16 1.Sri Lanka 1.65 2.16 0.98 1.16 1.49 0.94 1.89 1.72 1.07 1.03 0.

Taiwan 2.46 2.31 1.96 1.67 1.61 1.67 1.59 1.46 1.43 1.30 1.

Thailand 2.64 2.33 2.08 1.61 1.57 1.52 1.28 1.13 1.01 1.06 1.

Turkey 1.35 1.91 1.34 1.58 1.25 1.43 1.37 1.29 1.40 1.85 -0.

Venezuela 0.21 0.49 0.41 0.37 0.85 0.42 0.53 0.58 0.22 0.27 -0.

Zimbabwe 1.27 1.24 0.83 1.01 0.62 0.485 0.51 0.285 0.31 0.38 0.

Number (and percentage) of countries with year 1 M/B higher than year 10 M/B

Number (and percentage) of countries with statistically significant M/B changes

This table presents the medianmarket to book ratio (Datastream mnemonic MTBV) in 52 countries for firms in ages rangincolumn shows the number of firms for which Datastream has MTBV. Data are winsorized at 1st and 99th percentiles of MT

data entry errors. Sample period ranges from 1981 to 2004. The first appearance of a firm is used as a proxy for the firm

calculating its age. Ratios for US firms, shown in bold font, are reproduced from the Pastor and Veronesi (2003) articl

valuation is defined as the difference between year 1 M/B and year 10 M/B. We indicate statistical significance of the diffe

with ***, **, *, respectively.


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Table 3

Clustered standard errors regression analysis of a firms M/B ratio and its age in a global samp

Intercept AGE DD LEV SIZE ROE ROE(1) ROE(2) ROE(3) RET(1) RET

Panel A: All firms

Coefficient 0.203 -0.813 -0.052 0.026 0.009 0.241 0.569 0.413 0.114 -0.373 -0.3

T-statistic (5.02) (-17.22) (-3.07) (0.53) (3.70) (9.74) (19.73) (18.92) (6.86) (-45.04) (-38

Panel B: Developed markets firms

Coefficient 0.177 -0.686 -0.145 0.072 0.018 0.258 0.538 0.400 0.113 -0.364 -0.2

T-statistic (4.02) (-13.00) (-7.09) (1.34) (7.21) (8.66) (15.05) (15.07) (5.42) (-36.23) (-28

Panel C: Emerging markets firms

Coefficient 0.569 -1.673 0.136 -0.129 -0.039 0.268 0.670 0.448 0.112 -0.413 -0.3

T-statistic (5.58) (-16.61) (5.08) (-1.23) (-6.37) (7.07) (15.92) (12.34) (4.24) (-30.32) (-29

The following panel regression is estimated on pooled dataset while using clustered standard errors:

log(M/B)i,t = a + b.AGEi,t + c.DDi,t + d.LEVi,t + e.SIZEi,t + f.ROEi,t + g.ROE(1)i,t + h.ROE(2)i,t + i.R

+ j.RET(1)i,t + k.RET(2)i,t + l.RET(3)i,t + i,t

where (i = 1- N, N is the number of firms). M/Bi,t is the market to book ratio for firm i in period t. AGE is de

which captures the convex relationship between a firms M/B and its age according to the Pastor and Veronesiis the dividend dummy with value 1 for dividend paying firm and 0 otherwise. LEV is the debt ratio. SIZE is

total assets. ROE is the return on equity and regressed up to three years following year t. RET is future annual

from current period. i,t is the error term, which we cluster in SAS using proc surveyreg. All variables of

measured in its own currency. These regressions are based on 10,656 international firms for which historic

model are available in Datastream. T-statistics are reported in parentheses.


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Table 4

The effect of dividend payment on the learning process and price multiples

Intercept AGE DD AGE.DD LEV SIZE ROE ROE(1) ROE(2) ROE(3) RET(1)

Panel A: All Sample

Coeff. 0.134 -1.218 0.04 0.564 0.027 0.009 0.239 0.569 0.413 0.113 -0.373

T-stat (3.06) (-12.97) (1.50) (19.78) (0.55) (3.69) (9.73) (19.78) (18.97) (6.83) (-45.07)

Panel B: Developed market firms

Coeff. 0.103 -1.129 -0.05 0.60 0.072 0.018 0.257 0.539 0.401 0.113 -0.364

T-stat (2.13) (-10.10) (-1.59) (5.07) (1.33) (7.23) (8.69) (15.12) (15.14) (5.42) (-36.30)

Panel C: Emerging market firms

Coeff. 0.561 -1.722 0.15 0.079 -0.129 -0.039 0.267 0.67 0.448 0.112 -0.413

T-stat (5.23) (-11.13) (3.19) (0.43) (-1.23) (-6.37) (7.06) (15.93) (12.34) (4.24) (-30.24)

The following panel data regression is estimated using the pooled dataset identical to one used in the p

errors are clustered as suggested by Petersen (2009):

log(M/B)i,t = a + b.AGEi,t + c.DDi,t + e.DD.AGEi,t + f.LEVi,t + g.SIZEi,t + h.ROEi,t + i.RO+ k.ROE(3)i,t + l.RET(1)i,t + m.RET(2)i,t + n.RET(3)i,t + i,t

The term DD.AGE captures the incremental effect of dividend payment on the learning process. Rest definitions from the previous table.


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Table 5

The learning process and declining analyst forecast errors with progression in a firms age

Intercept AGE SIZE LEV RETVOL

NUMEST

DD ROE ROE(1) ROE(2) ROE(3) RE

Panel A: All Firms

Coeff.

T-stat.

0.093

(19.70)-0.018

(-8.57)

Coeff.

T-stat.

0.07

(6.23)-0.014

(-6.18)

-0.001

(-1.32)

0.007

(0.68)

0.402

(13.5)

-0.002

(-6.92)

Coeff.

T-stat.

0.092

(7.99)-0.013

(-5.86)

-0.013

(-5.86)

0.002

(0.17)

0.32

(10.1)

-0.002

(-6.35)

-0.005

(-1.14)

-0.071

(-9.30)

-0.053

(-6.17)

-0.012

(-1.47)

-0.0004

(-0.05)

0.0

(3.

Panel B: Developed markets

Coeff.

T-stat.

0.087

(18.69)-0.016

(-7.67)

Coeff.

T-stat.

0.063

(5.66)-0.012

(-5.43)

-0.001

(-0.90)

0.012

(1.23)

0.377

(12.5)

-0.002

(-7.43)

Coeff.

T-stat.

0.09

(7.73)-0.011

(-5.04)

-0.001

(-0.93)

0.005

(0.54)

0.284

(8.78)

-0.002

(-6.80)

-0.008

(-1.92)

-0.071

(-9.44)

-0.052

(-6.02)

-0.011

(-1.40)

-0.001

(-0.14)

0.0

(2.

Panel C: Emerging markets

Coeff.

T-stat.

0.395

(5.96)-0.141

(-4.12)

Coeff.T-stat.

0.729(5.18)

-0.136(-4.00)

-0.0229(-3.18)

-0.186(-1.25)

0.587(2.58)

0.002(0.85)

Coeff.

T-stat.

0.711

(4.61)-0.132

(-3.88)

-0.027

(-2.89)

-0.142

(-0.95)

0.493

(2.12)

0.002

(0.80)

-0.001

(-0.02)

-0.13

(-1.73)

-0.05

(-0.77)

-0.048

(-0.64)

0.046

(0.49)

0.1

(3.2


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Table 5Continued

Intercept AGE SIZE LEV RET

VOL

NUM

EST

DD ROE ROE(1) ROE(2) ROE(3) RE

Panel D: US market

Coeff.T-stat.

0.066(19.70)

-0.015

(-9.69)

Coeff.

T-stat.

0.035

(4.03)-0.014

(-8.91)

0.0003

(-0.45)

0.043

(5.93)

0.269

(11.2)

-0.001

(-4.49)

Coeff.

T-stat.

0.048

(5.31)

-0.013

(-8.31)

0.0001

(0.12)

0.38

(5.25)

0.241

(9.47)

-0.001

(-3.89)

-0.005

(-1.49)

-0.056

(-9.80)

-0.019

(-2.91)

-0.009

(-1.40)

0.002

(0.43)

0.0

(2.5

The following OLS regression captures the relationship between analyst errors in forecasting a firms EPS and the

FEi,t = a + b.AGEi,t + c.SIZEi,t + d.LEVi,t + e.RETVOLi,t + f.NUMESTi,t + g.DDi,t + h.ROEi,t + i.R

+ j.ROE(2)i,t + k.ROE(3)i,t + l.RET(1)i,t + m.RET(2)i,t + n.RET(3)i,t + i,t

where FEi,t is analyst forecast error for firm i in yeart; it is calculated as the absolute difference between m

actually reported EPS, scaled by the year-end stock price. AGE is defined as the natural log of age (fir

Datastream dataset). LEV is the debt ratio. SIZE is the natural log of the firms total asset. RETVOL is simple

as defined by the standard deviation of monthly returns during the observation year. NUMEST is the num

predicting EPS for the relevant period (i.e., analyst coverage). There are 14,594 firm-year observations in osample. White-adjusted standard errors are used to calculate t-statistics reported in the parenthesis.


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Table 6

Learning environment and analyst forecast errors

Analyst Errors

when Insider

trading law is

enforced

Analyst Errors

when Shortselling

is feasible

Analyst Errors

when Foreign

trading is above

median

Intercept 0.115

(9.50)

0.114

(9.41)

0.116

(9.79)

Size -0.016

(-8.28)

-0.015

(-7.46)

-0.016

(-8.47)

Leverage 0.031

(3.67)

0.027

(3.19)

0.046

(5.51)

Return Volatility 0.516

(21.12)

0.493

(19.99)

0.475

(19.87)

Number of Analysts -0.001

(-3.94)

-0.001

(-4.55)

-0.001

(-2.54)

ENVIRONMENT*AGE -0.005

(-2.62)

-0.006

(-3.24)

0.101

(37.85)

ANTI.ENVIRONMENT

*AGE

0.077

(16.91)

0.062

(12.15)

-0.010

(-5.24)

Adjusted R-squared 0.05 0.04 0.10

The following simple ordinary least squares regression model is estimated to capture the effects of learning

environment on the relationship between analyst forecast errors for a firms EPS and that firms age:

FEi,t = a + b.Sizei,t + c.Leveragei,t + d.Return Volatilityi,t + e.Number of Analystsi,t

+ f.ENVIRONMENT.AGEi,t + g.ANTI.ENVIRONMENT.AGE i,t + i,t

where FEi,t is analyst forecast error for firm i in year t; it is calculated as the absolute difference between

median forecasted EPS and the actually reported EPS, scaled by the year-end stock price.. Size is the naturallog of the firms total asset. Leverage is the debt ratio. Return Volatility is defined as the standard deviation

of monthly returns during the observation year. Number of analysts involved in predicting EPS for therelevant period is the proxy for analyst coverage. Age is defined as 1 in the first year of appearance of a firm

in the Datastream dataset and incremented by 1 in each year thereafter. Separate regressions are estimated for

each learning environment. For insider trading law, Environmentequals 1 if insider trading law is enforced

and 0 otherwise. Anti.Environement is the complement of environment. Both environment and

anti.environment are interacted with AGE. The interactive variables are computed analogously for the othertwo learning environment features. For shortsell feasibility, environment equals 1 if shortselling transactions

are allowed and 0 otherwise. For foreign trading, environment equals 1 if foreign institutional traders are

active in the countrys market and 0 otherwise. All variables of firms in a given country are measured in its

own currency. There are 20,416 firm-year observations in our Datastream-IBES merged sample. We useWhite-adjusted standard errors to calculate t-statistics reported in the parentheses.


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Table 7

Incremental effect regression: Impact of learning environment on valuation

Valuation Speed AGE E = Learning

environment

E*AGE Adj. R2

Panel A: All countries

Insider trading law enforced -0.217

(-7.02)

0.039

(1.71)

-0.16

(-3.97)

0.27

Shortselling feasible -0.631

(-12.63)

0.068

(1.81)

0.338

(6.22)

0.27

Foreign trading -0.449

(-16.65)

0.108

(3.68)

0.169

(4.20)

0.27

Panel B: Developed markets


(-2.88)

0.095

(3.40)

-0.237

(-6.32)

0.29


(-0.54)

0.03

(0.06)

-0.253

(-3.25)

0.28

Foreign trading -0.389(-14.25)

0.018(0.59)

0.188(4.68)

0.29

Panel C: Emerging markets


(-6.03)

-0.346

(-4.03)

-0.398

(-3.18)

0.24


(-13.65)

-0.112

(-0.85)

0.518

(3.13)

0.22

Foreign trading -0.707

(-9.14)

0.67

(5.28)

0.002

(0.01)

0.25

We define Equilibrium Valuation Speedas the rate of change of M/B ratio (i.e., log(M/B) t -

log(M/B)t-1) and regress it on various explanatory variables focusing on firms age and thelearning environment. The interactive variable specification follows the methodology of He and

Ng (1998):

Equilibrium Valuation Speed = c0 + c1Agei + cd0Environment + cd1Environment*Agei + c2DDi

+ c3LEVi + c4SIZEi + c5ROEi + c6ROE(1)i + c7ROE(2)i

+ c8ROE(3)i + c9RET(1)i + c10RET(2)i + c11RET(3)i+ cd2E DIVi + cd3E.LEVi + cd4E.SIZEi + cd5E ROEi

+ cd6E ROE(1)i + cd7E ROE(2)i + cd8E ROE(3)i

+ cd9E RET(1)i+ cd10E RET(2)i + cd11E RET(3)i + i

where Age and other base variables retain their definitions from Table 3 and interactive

variables are obtained by multiplying the value of Environment variable with the base variable.Environment (E) represents the learning environment indicator variable as defined in Table 6.

For example, E equals 1 if insider trading law is enforced in a given country in a given year and

0 otherwise and then that value is assigned to all applicable firm-year observations. All

variables of firms in a given country are measured in its own currency. There are 9,640 firms

(68,034 firm-year observations) with valid data for the whole sample, and 6,631 and 3,009

representing developed and emerging markets respectively. For brevity, we report only three

regression coefficients AGE E and AGE*E All t statistics reported in parentheses are based

Documents

The Speed of Learning About Firms' Profitability and Their Price Multiples a Global Perspective