Peter D. EASTON and Mark E. ZMIJEWSKI

Transcription

1 Journal of Accounting and Economics 11 (1989) North-Holland CROSS-SECTIONAL VARIATION IN THE STOCK MARKET RESPONSE TO ACCOUNTING EARNINGS ANNOUNCEMENTS* Peter D. EASTON and Mark E. ZMIJEWSKI ljniversi1.v of Chicago, Chicago, IL 60637, USA Received July 1986, final version received February 1989 Studies of the information content of accounting earnings typically assume earnings response coefficients do not vary across firms. Valuation models relating earnings to security prices, however, predict that earnings response coefficients are positively associated with revision coefficients (coefficients relating current earnings to future earnings) and negatively associated with expected rates of return. A random coefficient regression model provides evidence consistent with these predictions. This evidence has implications for interpreting multiple regression models that relate abnormal returns to unexpected earnings and other information variables. 1. Introduction and summary This paper focuses on the coefficient relating the surprise (new information) in accounting earnings announcements to abnormal stock returns. This coefficient measures the response of stock prices to accounting earnings announcements and we refer to it as the earnings response coefficient (hereafter, ERC). Most studies that examine the association between unexpected earnings and abnormal stock returns assume, at least implicitly, that ERCs are the same for all firms.* This study provides evidence that ERCs vary cross-sectionally and in a predictable manner. *The authors would like to acknowledge comments from workshop participants at the following universities: Arizona, Berkeley, British Columbia, Chicano. Purdue, Wisconsin. and Stanford. We extend thanks to A. Alford; W. Beaver, L. Ederington, W. Ferson, R. Freeman, J. Hughes, R. Kohn, B. Kross, T. Lys, J. Ohlson, S. Ryan, K. Schipper, A. Smith, S. Sunder, R. Watts, P. Wilson, M. Wolfson, R. Ball and S.P. Kothari (the referees), and especially to C. Ansley, R. Holthausen, and R. Leftwich for suggestions that have had a substantial effect on this paper. An alternative approach is to examine the association between stock price changes and unexpected earnings over a long period, say, twelve months. This alternative method does not examine the informational role of accounting earnings in valuation, rather, it examines the ability of accounting earnings to summarize the information that arrives during this period. Some examples are Beaver, Lambert, and Morse (1980) and Hagerman, Zmijewski, and Shah (1984); some exceptions are Magee (1975) Easman, Falkenstein, and Weil (1979). Kormendi and Lipe (1987), and Lipe (1986) /89/$ , Elsevier Science Publishers B.V. (North-Holland)

2 118 P.D. Euston and M.E. Zmijewski, Vnrintion in murket response to earnings The intuition for the empirical tests follows. Assume stock price equals the discounted value of expected dividends. If information in earnings announcements results in revisions of expected dividends, then stock prices will react to earnings announcements. The magnitude of the reactions is a function of the magnitude of the revisions. Larger revisions result in larger stock price reactions. The discounted value of the revisions depends on the expected rate of return. The higher the expected rate of return, the smaller the stock price reaction. Empirically, large revisions in expected earnings suggest large revisions in expected dividends. Thus, we expect ERCs to be an increasing function of the extent to which the information in an earnings announcement results in a revision in expected earnings (the revision parameter)3 and a decreasing function of the expected rate of return. Tests of these two relations require empirical distributions of ERCs, revision parameters, and expected rates of return. The empirical distribution of ERCs is estimated using an abnormal returns model. The slope coefficient from a regression of abnormal stock returns on a measure of unexpected earnings is used as the estimate of the ERC. We test both a two-day and a forecast-date abnormal return holding period; the two-day holding period includes the day before and the day of the earnings announcement, the forecast-date holding period extends from the day after the announcement of the forecast through the day of the earnings announcement (the average length of this period is 39 days).4 The revision parameter is estimated using two methods. The first method uses the parameter from Foster s (1977) time-series model for quarterly earnings. The second, the revision method, uses the slope coefficient from a regression of analysts revisions in forecasts of next quarter s earnings on analysts most recent forecast errors. If analysts use the Foster model to forecast quarterly earnings, the two methods estimate the same coefficient. Systematic risk (beta) is used as a proxy for cross-sectional variation in expected rates of return. Empirical tests are based on the Swamy (1970) random coefficient model. This model assumes the parameters are stationary over time but vary across firms. The random coefficient model is appropriate for two reasons. First, the paper focuses on cross-sectional variation in ERCs. Predictions of individual firm parameters from a random coefficient model are more efficient than predictions from ordinary least squares regression. Second, predictable crosssectional variation in the response coefficient is inferred from the correlations among the time-series parameters. Cross-sectional correlations among the 3Miller and Rock (1985) refer to this parameter as persistence. 4Unadjusted returns, first differences, and levels estimation methods are also examined. These alternative estimation methods yield results that are qualitatively identical to the results using the abnormal returns method.

3 P. D. Eaton und M. E. Zmijewski, Vurrution m market response to eclmrngs 119 time-series coefficients from random coefficient regressions have well-defined properties. The results indicate ERCs and revision parameters are positively correlated and ERCs and systematic risk are negatively correlated, although the statistical significance of this correlation is sensitive to the estimation method used.5 Attempts to control for the error in measuring the unexpected earnings by conditioning on firm size do not affect the inferences regarding these correlations. Cross-sectional variation in the ERC has implications for studies that constrain ERCs to be identical for all firms. This issue may not be critical in univariate regression models because the effect of the constraint is an inefficient estimate of the cross-sectional mean. For multiple regression models, however, information in earnings may be ignored and other explanatory variables may have significant (nonzero) coefficients because they capture cross-sectional variation of the ERC around the mean6 2. Conceptual framework Garman and Ohlson (1980) and Ohlson (1987a,b, 1988) present theoretical models that may be used to derive response coefficients for information variables (for example, the ERC for accounting earnings). These models demonstrate that (stock) price is a function of all information variables that predict dividends. If the system of time-series processes for the information variables that predict dividends is linear, then price may be expressed as a linear function of these information variables. For example, in the Garman and Ohlson framework, if there are * information variables for firm j, at time f, that predict dividends (Z+,,, 4 = 1,..., S) of which Zl,r is accounting earnings (A,,), then price at time t (P,,) may be expressed as P,~ = CJo + C,,A,, + C,&,r c,~z b,t. (1) The C,+s are the response coefficients of which C,, is the ERC. Response coefficients can be characterized as capitalization factors for the information variables. The response coefficients are a function of risk and the time-series 5Kormendi and Lipe (1987) also examine cross-sectional variation in ERCs using annual abnormal returns and a two-period distributed lag annual earnings time-series. The results indicate a positive correlation between ERCs and their measure of persistence. Collins and Kothari (1989) extend this research by examining additional factors that explain both cross-sectional and intertemporal variation in ERCs. For example, Holthausen (1981) regresses abnormal returns on unexpected earnings. public debt, and other financial variables for a cross-section of firms that switched back to straight-line depreciation methods. Holthausen observes a negative coefficient for the public debt variable when a positive coefficient is predicted. A potential explanation for this result is that the public debt variable is negatively correlated with the cross-sectional variation in the ERC. Easton (1987) provides evidence consistent with this explanation.

4 120 P. D. Easton and hf. E. Zmijewski, Variation in market response fo earnings parameters relating the information variable to future dividends and future information variables [see Garman and Ohlson (1980)]. For example, the ERC, C i, is a function of risk and of the time-series parameters relating accounting earnings to future dividends, future accounting earnings, and future nonearnings information variables that predict dividends ( Z+it, 4 = 2,..., 9). The abnormal return from period t - (Y through t [realized return, rjt, less expected return, E,_,( rj,)] is + cj2[ z*jt- Et-a(ZZjr)]/pjt-a + **. +Cj~[Zyjr-E,-.(Z~jr)]/~jr-,. (4 Eq. (2) formalizes the intuitive notion that the abnormal return over a specified period may be written as a linear function of the new information that arrives during that period. The weights or capitalization factors for the information variables are the respective response coefficients. If there is no surprise in the nonearnings information variables that arrive during the period, then the abnormal return is equal to unexpected earnings multiplied by the ERC, that is, C,i[ Aj, - E,_,( A,)]/,,_.. The exact form of the ERC cannot be derived unless the entire system of time-series processes for all of the information variables that predict dividends is known. Assuming the general system of time-series processes in Garman and Ohlson (1980) the signs of the partial derivatives cannot even be evaluated because the response coefficients (ERC) are too complex. Under some restrictive assumptions, however, the signs of the partial derivatives of the ERC can be evaluated. We test two hypotheses in this study: ERCs are increasing in the revision parameter and decreasing in risk. One set of assumptions that yield these predictions are the assumptions underlying the earnings capitalization model [Miller and Modigliani (1961)]. Earnings capitalization implicitly assumes that earnings is the only information variable that is needed to predict dividends; all other information variables are redundant. Accounting earnings is assumed to measure the earnings that are capitalized in this model plus some random error in measurement. A less restrictive set of assumptions is that earnings does not predict any of the nonearnings information variables in eq. (1). Even under these restrictive assumptions, however, the form of the ERC depends on JZq. (2) assumes that no dividends are paid during the return holding period. *See Ohlson (1983) for a discussion of these assumptions.

5 P. D. Easton and M. E. Zmijewski, Variation in market response to earnings 121 the assumed time-series process of earnings. Different time-series processes result in different ERCs. Thus, the range of forms (and, therefore, magnitudes) of the ERC is infinite. 3. Empirical models Empirical tests require estimates of ERCs, revision parameters, and risk. Methods used to obtain these estimates are described in this section. Since all estimation procedures have econometric problems that potentially result in biased and/or inefficient estimates, alternative methods are used to examine the consistency of the results. Correlations among the time-series coefficient estimates are estimated using a random coefficient regression model developed by Easton (1987). The model facilitates joint estimation of several time-series and cross-section regressions while providing statistical tests of the correlations among the coefficients in the jointly estimated regressions. This procedure is outlined in the appendix Estimation of revision parameters The revision parameter is estimated via an analysts revision model and the Foster (1977) model. A revision model is appealing because of the intuition that ERCs reflect the extent to which unexpected earnings in the current period results in a revision in the forecasts of future earnings. The ideal model examines revisions in market forecasts made immediately before and after the earnings announcements. However, such forecasts are not available. Value Line analysts forecasts are used. These forecasts are generally made every 13 weeks. The revision models in this study regress analysts forecast revisions on their most recent earnings forecast errors plus a variable that proxies for nonearnings information analysts may use to forecast earnings during the 13-week period. The model for a one-quarter forecast revision horizon is REY., = O,, + OjlFEj, + 0j2PVLVLj, + ujt, and the two-quarter model is RE v,; = O;,, + 0;; FE,, + 0;; P VL VLjI + ujt, Further, analysts earnings forecasts are more accurate than time-series model forecasts and unexpected earnings are more highly correlated with abnormal returns around the earnings announcement when they are conditioned on analysts forecasts rather than time-series forecasts [Brown et al. (1987a, b)].

6 122 P. D. Easion und M. E. Zmijewskl, Variation in murket response to eumings Time Ajt-1 A,, A Jr+1 r-1 F /t r-1 F F Jf+l f Jl+l F F r-1 If+2 f J112 Fig. 1. Time-line for earnings forecasts. Variables in eqs. (3) and (4) are defined as FE,, = A,, -,~, F,,, REV,, =, F,, + I -,_, F,, +,, REV,; = f F,,+2 ~,~, F,,, 2. where A,, = announced earnings of firm.j in quarter t and, F,,,, = Value Line forecast of A,,,,, conditional on knowledge of A,,. where REY, = revision in the Value Line Investment Survey (Value Line) earnings forecast of firm j for quarter t + 1 following the earnings announcement in quarter 2, REY.; = revision in the Value Line earnings forecast of firm j for quarter t + 2 following the earnings announcement in quarter t, FE,, = announced earnings in quarter t minus the most recent Value Line forecast for quarter t earnings, PVLVL,, = change in stock price for firm j from the day after the Value Line earnings forecast date preceding the earnings announcement in quarter t through the day before the Value Line earnings forecast date immediately after the earnings announcement in quarter t, excluding the three days before, the day of, and the three days after the earnings announcement in @,I, Ojl, O,2, O/; = firm-specific regression coefficients, u,0 u,f = normally distributed disturbance terms. To clarify the calculation of FEjl, RET,, and REV,;, consider the time-line in fig. 1 where A,, is the announced earnmgs of firm j in quarter t and IFJI+T is the Value Line forecast of AJf+T, conditional on knowledge of A,. The variables in eqs. (3) and (4) are defined as

7 P. D. Euston and M. E. Zmijewski, Van&ion in murket response 10 ecrrnings 123 The results in Brown and Rozeff (1979) suggest that analysts use an autoregressive time-series process. A method of testing this hypothesis is to compare revision parameters (O,,) from a one-quarter horizon revision model to revision parameters from a two-quarter horizon model; such tests are conducted in this study. These revision models are consistent with analysts forecasting earnings using a first-order autoregressive or a seasonal first-order autoregressive time-series process [for example, Foster (1977)]. To the extent that analysts use information that is not contained in Pl LW,, (that is, information that is not implicitly captured by price) there is a potential omitted variables problem in eqs. (3) and (4). Predictions regarding the coefficients in eqs. (3) and (4) follow. First, O,, = 0,; = 0 because the time-series process is estimated in revision form. Second, O,i is less than 1.0. Easton and Zmijewski (1987) demonstrate that O,i less than one plus the expected rate of return is sufficient for ERCs to be strictly positive for many theoretical frameworks. Third, O,, > 0 because future earnings changes are generally positively related to stock price changes [see Ball and Brown (1968)]. Finally, O, i = (0,1)2; again, since the univariate time-series process for earnings may be characterized as a seasonal first-order autoregressive model [Foster (1977)] and because Value Line forecasts are consistent with an autoregressive time-series process [Brown and Rozeff (1979)]. However, since analysts use nonearnings information to forecast earnings (for example, PVLIX,,), an exact equality is not expected. The Foster model is the second method for estimating the coefficient relating current earnings to future earnings. That is, A jl+l - Ajt-3 =OJb +0:1 = firm-specific regression coefficients, normally distributed disturbance term. U,I = Jf This model ignores the role of nonearnings information in forecasting earnings that is modelled in the time-series process in eq. (3). If analysts use the Foster (1977) model to predict earnings, 0;; is identical to O,i Estimation of earnings response coeficients The ideal ERC estimation method conditions unexpected earnings on the market s expectations of earnings immediately before the earnings announcement and measures abnormal returns immediately around the earnings announcement. Further, ideally no other information arrives contemporaneously with earnings. As a practical matter, however, these data are not available.

8 I24 P. D. Easton and M. E. Zmijewski, Variation in market response to earnings Alternative estimation models are available but all of these suffer from either measurement error and/or omitted variable problems. Analysts forecasts (that are on average 39 days old) are used as the measure of expected earnings. Use of this forecast creates a trade-off when constructing the abnormal return metric. If a two-day (forecast-date) holding period is used, there are fewer (more) confounding events affecting the stock return but there is more (less) measurement error in unexpected earnings. We examine three alternative measures of abnormal returns; market model prediction errors, realized returns, and mean return prediction errors. The trade-offs among these measures are discussed below. The distribution of ERCs for a sample of firms is estimated via an abnormal returns model with a two-day holding period and an abnormal returns model with a forecast-date holding period. These models are, respectively, and where CPE(s, 0),, = sum of the market model prediction errors over the interval extending from trading day s through the earnings announcement day for firm j for quarter t in the Wall Street Journal (WSJ), day 0 [day s is either the day before the earnings announcement (- 1) or the day after Value Line reports its forecast (VL)], js-1 = price of security j on day s - 1, R VL,, = stock return for firm j from the day after the Value Line report date through two days before the earnings announcement, jo3 JO5 j1> h)lt ~2 = firm-specific regression coefficients. P,r, l$t = normally distributed disturbance terms. The two-day (- 1,O) period reduces the possibility that other information arrives within the abnormal return holding period. The most recent Value Line The market model is estimated over days -360 through -61 (where day 0 is the earnings announcement date) using the CRSP Equally Weighted Stock Index as the measure of market return. To be included in the sample, a firm must have at least 100 return observations over the market model estimation period and all returns over both cumulation periods. The results are qualitatively identical using mean-adjusted returns, market-adjusted returns, or unadjusted returns.

9 P. D. Easton and M. E. Zmijewski, Variarion in market response to earmngs 125 forecast of earnings is used as a proxy for the market s expectation of earnings at the beginning of this holding period. There is error in measuring these expected earnings since these forecasts are made before day - 1. This measurement error problem is mitigated if an additional independent variable, that is correlated with the measurement error in unexpected earnings but uncorrelated with the dependent variable, is included in the regression. The stock return from the day after the Value Line report date through two days before the earnings announcement, RVLj,, is used for this purpose [see eq. (9)]. This return is positively correlated with measurement error if earnings forecast revisions occurring between the Value Line forecast date and the day before the earnings announcement are positively correlated with the stock return over this period. If this procedure is successful in reducing measurement error, then Xj, should be negative. An alternative solution to this problem is to use a holding period from the Value Line forecast date to the earnings announcement date [see eq. (lo)]. However, increasing the holding period increases the likelihood that other information is released during the holding period, potentially resulting in an omitted variables problem.13 Predictions for the coefficients in eqs. (9) and (10) follow. First, X,, = X)0 = 0. The finding of a nonzero intercept coefficient would suggest a correlated omitted variables problem in eq. (9) or (10). Second, Xj, > 0. Sufficiem (and plausible) conditions for a positive ERC are described in Easton and Zmijewski (1987). Third, Xi, < 0, since stock returns are positively correlated with the measurement error in unexpected earnings [Brown et al. (1987b)]. Eq. (2) defines abnormal returns as realized returns less expected returns. In this paper, market model residuals are used as the measure of abnormal returns. Market model residuals, however, are conditioned on ex post market returns, not expected market returns. The difference (for firm j in return period t) between the market model residual (that is, prediction errors conditioned on ex post market returns), E/~, and the market model prediction error conditioned on expected market returns, vjt, is - p,( R,,,, - E( R,,)), that is, El, = Vj, - Pj(R,, - E(R,,)); see Watts and Zimmerman (1986, pp ) for further discussion. Conditioning market model prediction errors on ex post market returns biases the ERC estimates if the market s measure of unexpected earnings is correlated with the unexpected market return. The problem is not solved by conditioning unexpected earnings on ex post market earnings because this approach, although it eliminates the inconsis- See Brown et al. (1987b) for details. 13For the sample of observations in this paper, this forecast horizon is. on average, 39 days. Extending the holding period to the analyst s forecast date assumes the analyst s forecast is an appropriate measure of market s expectation of accounting earnings. Extending the holding period before the analyst s forecast date does not appropriately control for differences between the analyst s forecast and the market s expectations at the forecast date. Such a metric introduces both measurement error and omitted variables problems.

10 126 P. D. Euston and M. E. Zmijewski, Variation in mcrrket response to eurnings tency in measurement, eliminates any relation between unexpected market returns and the market s measure of unexpected earnings in the ERC estimates. An alternative approach uses realized returns. This approach induces a spurious relation if the measurement error in unexpected earnings is correlated with expected market returns or the parameters of the market model. Ideally, one would use expected market returns when measuring market model prediction errors. Such expectation models, however, are not readily available. One alternative is the mean return model. This model assumes that expected market returns equal the mean market return over some previous period. Measurement error in the mean return model that is correlated with the measurement error in unexpected earnings results in biased ERC estimates. We conjecture that the bias resulting from using market model prediction errors is most severe when the abnormal return holding period begins during the earnings fiscal period. For example, assume the holding period begins on the first day of the fiscal year and ends on the earnings announcement date. Unexpected earnings is conditioned on information existing on the first day of the fiscal year in this analysis. It is likely the case that the unexpected market returns over this holding period are correlated with unexpected earnings because both the market and the firm s operations are affected by the same economy. As an alternative, assume that the holding period is restricted to the earnings announcement date. Unexpected market returns are less likely to be correlated with unexpected earnings because the earnings are less likely to be affected by unexpected changes in the economy after the close of the fiscal period. Also, we conjecture that the spurious relation resulting from using realized returns is most severe when forecasting market expectations using univariate time-series models. Univariate time-series models ignore the information in expected market returns that is related to expected earnings. Thus, measurement error in univariate time-series model forecasts are likely to be correlated with unexpected market returns. Analysts forecasts, however, are less likely to ignore the information in expected market returns. These problems suggest potential reasons for using market model prediction errors, realized returns, and mean return prediction errors. The problems using these methods are mitigated using short holding periods and analysts forecasts. We examine all of these methods but report only the results based on market model prediction errors. All of these methods yield qualitatively identical results Estimation of systematic risk Cross-sectional variation in expected quarterly rates of return is assumed to be captured by cross-sectional variation in systematic risk as estimated by the

11 P. D. Euston and M. E. Zmijewski, Variution in market response to earnings 121 market model. The market model may be written as where R,, = a, f P,R,, + e,,, 01) RJt = continuously compounded rate of return on the common stock of security j for quarter t, R,,,, = continuously compounded rate of return on the CRSP Equally Weighted Index for quarter 1, (yj = intercept coefficient, p, = slope coefficient (and estimate of systematic risk) for firm j, = normally distributed disturbance term. ejt 4. Data and sample selection Data in this study are a subsample of the data in Brown et al. (1987a). Value Line forecasts for the six-year period were collected. All firms included in the Brown et al. sample satisfy three criteria: (1) quarterly earnings per share available in Moody s Handbook of Common Stocks, (2) the same fiscal year end between 1960 and 1980, (3) covered by Value Line between 1975 through The number of firms satisfying these criteria is 212. For a firm to be included in the sample for this study, a firm must also have complete data for 20 quarters for the following:i4 (4) WSJ earnings announcement date available in the Wall Street Journal Index, (5) data available from Value Line to calculate FE,, and REV,,, (6) stock price available on the CRSP Daily Master File for the day before the CPE( s, 0),, cumulation periods (day s - l), (7) sufficient stock return data available on the CRSP Daily Return file to calculate the market model prediction errors needed to calculate both CPE(s, O),,s and the quarterly R,,, (8) earnings per share data available on the Compustat Quarterly Industrial File to estimate the Foster (1977) time-series model. r4the decision to require 20 quarters (observations) in the time-series is arbitrary. Requiring more (fewer) observations in the time-series results in a smaller (larger) sample of firms. More observations in the time-series increases efficiency but it also lengthens the period over which stationarity is assumed. Choices within the range of 18 through 23 observations do not alter the results.

12 128 P. D. Easton and M.E. Zmijewski, Variation in market response to earnings Depending on the specific set of models that are estimated, these selection criteria result in sample sizes ranging from 104 to 206 firms, with each firm having 20 (quarterly) time-series observations. 5. Empirical results The coefficient distributions for all time-series models are presented in tables 1, 2, and 3. These distributions are estimated for each model using the random coefficient procedure in Swamy (1970).15 Cross-sectional means, medians, 10th and 90th percentiles, and standard errors (of the means) are presented. Since data on medians and 10th and 90th percentiles generally do not suggest peculiarities in the distributions, they are not discussed in the text. 5. I. Earnings time-series model coeftfcients Table 1 summarizes the coefficient distributions for the three earnings time-series (revision) models [eqs. (3), (4), and (S)]. Panel A of table 1 presents these statistics for the one-quarter horizon revision model, eq. (3). Recall from section 3 that the intercept, OiO, is expected to equal zero if analysts use a first-order autoregressive time-series process to forecast earnings. The crosssectional mean intercept coefficient, ojo, is and its standard error is The null hypothesis that the mean intercept coefficient is zero, oio = 0.0, is rejected at less than the 0.05 probability level suggesting model misspecification. Two potential explanations for this result are that analysts use a time-series process different from an autoregressive model and/or relevant predictor variables have been omitted from the model. The coefficient relating analysts most recent forecast errors to analysts revisions, Ojl, is expected to be less than 1.0 if analysts use an autoregressive time-series process. The mean Ojr is and its standard error is The 99 percent confidence interval for the mean is I gjl and the null hypothesis that Gj, is rejected at less than the 0.01 probability level. These results are consistent with the results in Brown and Rozeff (1979) and indicate that, on average, a $1.00 shock in earnings leads to a revision of $0.344 in the expected earnings of next quarter. However, since this model is used to measure the market s revision parameters, coefficient estimates are potentially biased from measurement error and omitted variables. The distribution of the coefficients that are obtained from the joint estimation of the models that are used in calculating the correlations among the coefficients are not reported. However, the impact of the joint estimation procedure is minimal in each of the empirical models.

13 P. D. Easton and M. E. Zmijewski, Variation in market response to earnings 129 Table 1 Distributional characteristics of the coefficients of the time-series process for eamings..b Panel A: One-quarter revision coefficient (150 firms) Eq. (3): REV,,= O,,+ O,,FE,,+ O,,PVLVL,,+ u,! J1 0 /2 10th percentile Median th percentile Mean Standard error Panel B: Two-quarter revision coefficient (131 firms) Eq. (4): REV,; FE,, + 0, 2 PVLVL,, + u;, Q;O 0 /I Q/; 10th percentile Median th percentile Mean Standard error Panel C: Foster (1977) model revision coefficient (206 firms) Eq. (8): A,,+, - A,,_, = 0,; + 0, (( A,, -A,,_,) + u;, 0 JO 0 /I 10th percentile Median th percentile Mean Standard error Variable definitions: REV,, = revision of the forecast of firm j s next quarter earnings; FE,, = forecast error for quarter t earnings; PVLVL,, = change in stock price for firm J from the day after the previous Value Line earnings forecast date through the most recent Value Line earnings forecast date, excluding the three days before, the day of, and the three days after the earnings announcement that occurred during the period; A,, = accounting earnings of firm j in qubarter t. Estimation: Eqs. (3), (4). (8) are estimated using the Swamy (1970) random coefficient model on 150, 131, and 206 firms, respectively. Each firm has 20 time-series observations available between 1975 and The mean coefficient for the proxy for other information that is used by analysts to forecast earnings, O,2, is expected to be positive because extant empirical evidence indicates a positive association between stock price changes and changes in future earnings. The mean O,* is and its standard error is The null hypothesis that o/z 5 0 is rejected at less than the 0.05 probability level, which is consistent with analysts revising earnings forecasts in the direction of recent stock price changes.

14 130 P. D. Easton and hf. E. Zmijewskt, Variution in market response to earnings Eq. (4) examines a two-quarter horizon revision model. Panel B of table 1 presents results similar to those in panel A for this model. The mean coefficient relating analysts most recent forecast error to the revision, o,!i, is and its standard error is The 99 percent confidence interval for o,!i is I o,!i s If analysts use a first-order autoregressive time-series process for earnings, then the two-quarter horizon revision coefficient is equal to the square of the one-quarter horizon revision coefficient = (G,,,) ]. Recall that the 95 percent confidence interval for O,i in eq. (3) is from to This confidence interval implies that the range of (O,,) is from to The similarity of the confidence intervals for 0;1 and (O,,) is consistent with either a first-order or a seasonal first-order autoregressive characterization of the time-series process of quarterly earnings. Panel C of table 1 presents the distributional characteristics of the time-series parameters of the Foster model. The mean intercept, o$, is and its standard error is The 99 percent confidence interval is o,!h These results indicate that the intercept is reliably greater than zero which is consistent with both an omitted variables and errors in variables problem. The mean coefficient relating current earnings to future earnings, o, i, is and its standard error is The 99 percent confidence interval is I o/; I These results indicate that o/; is reliably greater than zero and that, on average, a $1.00 shock in this quarter s earnings results in a $0.486 revision in next quarter s earnings. Recall that if analysts use the Foster model to predict earnings, both the one-period ahead revision model and the Foster model estimate the same coefficient, O,i. Hence, both models provide an estimate of how a shock in earnings persists into the future. The revision model indicates that, on average, a $1.00 shock in this quarter s earnings results in a $0.344 revision in next quarter s earnings. The estimate of O,i from the revision model is less than the estimate from the Foster model. The null hypothesis that the mean coefficient from the revision model is equal to the mean coefficient from the Foster model is rejected at less than the 0.05 probability level. This result indicates that analysts assume a time-series process that differs from the Foster model or either the revision model or the Foster model is misspecified. These results do not, however, provide justification for relying on a particular model to estimate the revision parameter. Therefore, both models are used in the correlation tests Earnings response coeficients Table 2 presents distributional characteristics of the ERC estimates. The results for the two-day holding period, eq. (9), are presented in panel A of table 2. The mean intercept, xjo, is and its standard error is Thus,

15 P. D. Easton and M. E. Zmijewski, Variation in market response to earnings 131 Table 2 Distributional characteristics of the coefficients of the valuation model.a.b Panel A: Two-day holding period ERCs (172 firms) Eq.(9): CPE(-l,O),,=X,o+h,,[FE,,/P,,~,l+X,,RVL,,+~,, x JO x /I h 12 10th percentile Median th percentile Mean Standard error Panel B: Forecast-date holding period ERCs (158 firms) Eq. (10): CPQGO),, = p,, + ~,,[FE,,/p,,,_,I + II;, A,0 X Jt 10th percentile Median th percentile Mean Standard error Variable definitions: CPE(s,O),, = cumulated market model prediction error, cumulated from day s through the earnings announcement date, day 0 (VL is the day after the Value Line report date); FE,, = forecast error for quarter t earnings: qs_ 1 = price of security j on day s - 1; R VL,, = stock return for firm j from the day after the Value Line report date through two days before the earnings announcement. bestimation: Eqs. (9) and (10) are estimated using the Swamy random coefficient 172 and 15X firms, respectively. Each firm has 20 time-series observations available between 1975 and the null hypothesis that x,, = 0.0 cannot be rejected at normally acceptable probability levels. The mean ERC, xjl, is and its standard error is The 99 percent confidence interval for the mean ERC is I>,~ I and the null hypothesis that Ai1 I: 0.0 is rejected at less than the 0.01 probability level. The mean A,, is and its standard error is The null hypothesis that x, is rejected at less than the 0.05 probability level which is consistent with a positive association between the stock return before the abnormal return holding period and the measurement error in unexpected earnings. If increasing the abnormal return holding period reduces the measurement error in unexpected earnings, then, all else equal, the mean Xi, will increase (see section 3). However, a longer holding period increases the likelihood that nonearnings information arrives within the holding period. The results for the forecast date holding period, eq. (lo), are presented in panel B of table 2. The mean intercept, Rj,, is and its standard error is The null hypothesis that kj,, = 0.0 is rejected at the 0.01 probability level. This result

16 132 P. D. Easion and M.E. Zmijewski, Variation in market response to earnings (compared with failure to reject the same null hypothesis when the two-day window is used) is consistent with an omitted variables problem caused by a lengthening of the abnormal return holding period. The mean ERC using the forecast-date holding period, x,r, is and the standard error of the mean is Thus, the 99 percent confidence interval for x j1 is IX), I The null hypothesis that h), is rejected at less than the 0.01 probability level. The mean ERC for the forecast-date holding period, x)r, is greater than the mean ERC for the two-day holding period, x,r, versus 1.649, which is consistent with the measurement error discussion in section 3. However, the larger standard error of the slope coefficient and a nonzero intercept for the longer holding period are consistent with an omitted variables problem. The two distributions of ERCs differ considerably, as do the two distributions of revision coefficients. Since it is not possible to ascertain which estimates are less biased by econometric problems, all of the estimates are used when examining the correlations among the coefficients Systematic risk Finally, the distributional characteristics of the estimates of the market model coefficients are presented in table 3. Since the statistical properties of market model parameters are well known, they are not discussed in detail here. These results are consistent with the extant evidence except that the mean Table 3 Distributional characteristics of the coelhcients of the market model.a.h Eq. (11): R,, = cc, + b, R,,, + e,, (205 firms) a/ 4 10th percentile Median th percentile Mean Standard error Variable definitions: R,, = continuously compounded rate of return on the common stock of security j for quarter t; R,,, = continuously compounded rate of return on the CRSP Equally Weighted Index for quarter t. bestimation: Eq. (11) is estimated using the Swamy random coefficient model on 205 firms. Each firm has 20 time-series observations available between 1975 and 1980.

17 P. D. Easion and M. E. Zmijewski, Variation in market response to earnings 133 systematic risk in this sample, Bj, is which is less than one. However, the sample selection criteria in this study biases the sample towards large firms which are typically less risky Partial correlations Table 4 presents the partial correlation between the ERC and the revision parameter, conditional on systematic risk, p( h,i, Oji 1 p,), as well as the partial correlation between the ERC and systematic risk, conditional on the revision parameter, p( X,i, /3,] O,,). These correlations are presented for all possible combinations of the empirical models that are used to estimate these coefficients. Overall the results indicate a positive correlation between the ERC and the revision coefficient while the correlation between the ERC and systematic risk is negative. The largest correlation between the ERC and the revision coefficient is (standard error 0.106); the smallest correlation is (standard error 0.102). Although these tests are not independent, all correlations are positive indicating the ERC is an increasing function of the revision coefficient. The largest (in absolute value) correlation between the ERC and systematic risk is (standard error 0.120); the smallest correlation is (standard error 0.209). Although the tests are not independent and not all of the correlations are reliably different from zero, all correlations have the predicted negative sign Firm size as a control for measurement error Brown et al. (1987b) demonstrate a downward bias in ERC estimates caused by measurement error in empirical measures of unexpected earnings. Measurement error may affect the results in this study if it varies across firms and it is correlated with either the revision coefficient or systematic risk. We examine the potential effect of measurement error on the results by controlling for firm size (the market value of equity) in the partial correlation tests. Inclusion of a size variable relies on the conjecture that unexpected earnings measures for large firms have more error than those for small firms because more information is released between analysts forecast dates and earnings announcements The mean equity market value of this sample is greater than the 80th percentile of equity market values of all American and New York Stock Exchange firms.

18 134 P. D. Euston and M. E. Zmijewski, Variation in market response to earnings Table 4 Partial correlations between the earnings response coefficient and its determinants.., I/3,) Panel A: Two-day holding period ERCs [eq. (9)] (1) One-quarter revision coefficient [eq. (3)] P(X,,, P, Correlation Standard error (2) Foster (1977) model revision coefficient [eq. (g)] Correlation Standard error Panel B: Forecast-date holding period ERCs [eq. (lo)] (1) One-quarter revision coefficient [eq. (3)] Correlation Standard error (2) Foster (1977) model revision coefficient [eq. (g)] Correlation Standard error Equations: Eq. (3): REV,,=@,,+O,,FE,,+@,,PVLVL,,+u,,; eq. (8): A,,+, -A,,_?= Q, <; + Q;, ( A,, - A,,_,) + u;, ; eq. (9): CPE(-1,0),,=~,o+~,l[FE,,/P,,~21+~,2RVL,,+p,,; eq. (10): CPE(VL,O),,=X,o+X,,[FE,,/P,,,_,] +p;,; eq. (11): R,,=a, +/3,R,,,+ e,,. Variable definitions: REV,, = revision of the forecast of firm j s next quarter earnings; FE,, = forecast error for quarter t earnings; PVLVL,, = change in stock price for firm j from the day after the previous Value Line earnings forecast date through the most recent Value Line earnings forecast date, excluding the three days before, the day of, and the three days after the earnings announcement that occurred during the period; A,, = accounting earnings of firm j in quarter t: CPE(s,O),, = cumulated market model prediction error, cumulated from day s through the earnings announcement date, day 0 (VL is the day after the Value Line Report date): FE,, = forecast error for quarter r earnings; P,.Y _ 1 = price of security j on days - 1; R VL,, = stock return for firm j from the day after the Value Line report date through two days before the earnings announcement; R,, = continuously compounded rate of return on the common stock of security j for quarter 1; R,,, = continuously compounded rate of return on the CRSP Equally Weighted Index for quarter 1. Correlations are estimated using the Easton (1987) random coefficient procedure outlined in the appendix. p(x,,, 0 11 /I,) = correlation between X,, and O,,, conditional on b,; p(x,,, fi, 1 O,,) = correlatton b etween X,, and /1,, conditional on O,]. for large firms. That is, firm size is positively correlated with the measurement error variance in unexpected earnings and, hence, it is negatively correlated with the measurement error bias in ERG. Since firm size may also be associated with other economic characteristics of the firm, these tests are not strictly interpretable as tests controlling for Collins, Kothari, and Raybum (1987) provide empirical evidence consistent with this cometture.

19 P. D. Euston and M. E. Zmijewski, Variation rn market response to earmngs 135 measurement error. For example, it is well known that stock returns are negatively correlated with firm size. is Therefore, firm size may proxy for risk which would bias tests that examine the association between ERCs and systematic risk toward not finding an association. Given these alternative interpretations of firm size, it is not possible to predict the effect that controlling for firm size will have in the partial correlations. If firm size controls for the measurement error in unexpected earnings, the effect on the correlations cannot be predicted. Alternatively, if firm size is a more appropriate measure of cross-sectional variation in expected rates of return than is beta, then the correlation between the ERC and beta, conditional on the revision coefficient and firm size, will be zero, while the correlation between the ERC and firm size, conditional on the revision coefficient and beta, will be positive. To estimate these correlations, the following equation is added to the system of eqs. (3) (9) and (11) and the four equations are estimated jointly using the procedure described in the appendix: SizeJI = Size, + vj,, 02) where Size,, = natural logarithm of the market value of equity for firm j in quarter t, Size J = firm-specific regression coefficient, that is, mean Size,,, VII = normally distributed disturbance term. Three partial correlations are presented in table 5: (i) between the ERC and the coefficient relating current earnings to future earnings, conditional on firm size and beta [p(x,,, Oji I/3,, Size,)], (ii) between the ERC and beta, conditional on firm size and the revision coefficient [p(x,,, /?, 1 Ojl, Sizei)], and (iii) between the ERC and firm size, conditional on the revision coefficient and beta [ p( Xjl, Sizej 1 OJ1, /3,)]. Overall, the results regarding the correlations between the ERC and the revision coefficient are not affected when controlling for firm size. The largest correlation is (standard error 0.124) and the smallest correlation is (standard error 0.154). These results support the results in table 4. The partial (absolute) correlations with systematic risk generally decrease and the standard errors increase with the addition of firm size as a conditioning variable. None of these correlations is reliably different from zero. Simi- *See Schwert (1983) for a discussion of this literature

20 136 P. D. Easton and M. E. Zmdewski, Variation in market response to earnings Table 5 The impact of firm size on the partial correlations between the earnings response coefficient and its determinantsa Panel A: Two-day holding period ERCs [eq. (9)] (1) One-quarter revision coefficient [eq. (3)] Correlation Standard Correlation Standard Correlation Standard Correlation Standard error error error error (2) Foster (1977) model revision coefficient [eq. (S)] Panel B: Forecast-date holding period ERCs [eq. (lo)] (1) One-quarter revision coefficient [eq. (3)] (2) Foster (1977) model revision coefficient [eq. (S)] Equations: Eq. (3): REV,, + OJIFE,, + u,,; eq. (8): A,,+, -A,,_, = O/b + O;, (A,, - A,,_,) + u;;; eq. (9): CPE(-1,0),,=X,o+X,,[FE,,/P,,_21+h,zRVL,,+u,,; eq. (10): CPE( VL,O),, = X;,, + X,,[ FE,,/P,v,_,] + pl;,; eq. (11): R,, = uj + 4 R,,, + e,,; eq. (12): Size,, = Size, + u,,. Variable definitions: REV,, = revision of the forecast of firm j s next quarter earnings; FE,, = forecast error for quarter t earnings; PVLVL,, = change in stock price for firm j from the day after the previous Value Line earnings forecast date through the most recent Value Line earnings forecast date, excluding the three days before, the day of, and the three days after the earnings announcement that occurred during the period; A,, = accounting earnings of firm j in quarter r; CPE(s, 0),, = cumulated market model prediction error, cumulated from day s through the earnings announcement date, day 0 (VL is the day after the Value Line report date): FE,, = forecast error for quarter t earnings; qs _ r = price of security j on day s - 1; R VL,, = stock return for firm j from the day after the Value Line report date through two days before the earnings announcement; R,, = continuously compounded rate of return on the common stock of security j for quarter t; R,,, = continuously compounded rate of return on the CRSP Equally Weighted Index for quarter r; Size,, = natural logarithm of the market value of equity for firm,j in quarter r; Size, = firm-specific regression coefficient, that is, mean Sire,,. Correlations are estimated using the Easton (1987) random coefficient procedure outlined in the appendix. p(a,, b, 1 c,, d,) = correlation between a,, and h,,, conditional on c, and d,.