Moral hazard and the effects of the designated hitter rule revisited.

Goff, Brian L. ; Shughart, William F., II ; Tollison, Robert D. 等

I. INTRODUCTION

In a recent paper in this journal, we [Goff, Shughart, and Tollison 1997] hypothesized that the introduction of the Designated Hitter (DH) rule in the American League but not the National League of Major League Baseball in 1973 created the potential for a classic moral hazard problem. Because they are no longer required to appear at the plate, American League pitchers can throw at opposing hitters with greater impunity (i.e., at a lower cost) than National League pitchers, who still must take their turns at bat. The economic theory of moral hazard clearly predicts that more batters will be hit by pitches in the American League than in the National League under such circumstances, an implication that was supported by our empirical evidence, which covered the period running from the birth of the American League in 1901 through the end of the 1990 pennant campaign. After controlling for other relevant factors, we found that American League batters had been "plunked" at rates 10% to 15% higher than their National League counterparts in the typical regular baseball season since the DH rule went into effect.

Two comments published in this issue raise questions about the empirical magnitude of the DH effect and cast doubt on our interpretation of the evidence. In particular, relying on post-1990 data unavailable to us at the time our paper was in press, Levitt [1998] and Trandel, White, and Klein [1998] suggest that the differences in the rates at which batters are hit by pitches in baseball's two major leagues may no longer be statistically significant and, moreover, to the extent that they are, that these differences are better explained by post-1973 changes in the composition of American League batters than by the DH rule's effects on pitchers' own costs and benefits of throwing at opposing hitters. Levitt and Trandel, White, and Klein contend that the number of batters hit by pitches rose in the American League after 1973, not because pitchers had less to fear from retaliation directed against them personally, but because the substitution of hard-hitting DHs for weak-hitting pitchers made beanball more profitable: AL team managers had more to gain from placing designated hitters on base by instructing pitchers to plunk them than from giving free passes to pitchers, who otherwise represent easy outs.

In what follows, we explore the implications of this alternative hypothesis more fully. Because "better hitting in the American League" does not explain inter-league differences in hit batsmen prior to 1990, and because the DH rule continues to be a significant determinant of inter-league differences in hit batsmen after 1990 once exogenous events in the National League are taken into account, we conclude that our original interpretation of the empirical evidence stands.

II. WHAT HAPPENED IN THE 1990s?

Two stylized facts lead Trandel, White, and Klein to conclude that moral hazard explains little, if any, of the observed differences in hit batsmen between the American and National leagues. One is that, when our post-World War II subsample is expanded by adding data from regular season games played through August 31, 1997, at most only about 3% of the lower rate of hit batsmen in the National League can be attributed to the American League's adoption of the DH rule in 1973.(1) The other is that, while, consistent with our results, American League batters were in fact hit by pitches 12% more frequently over the 1947-1990 period, this empirical regularity can be explained better by inter-league differences in the composition of batters. In particular, Trandel, White, and Klein suggest that the evidence supports the following statement. "To the extent that American League batters are (on average) more likely to be hit by pitches than are National League batters, the difference is largely because the AL batters are (on average) better hitters, and are thus less costly and more beneficial to hit" (p. 679).(2) Trandel, White, and Klein buttress their conclusion that moral hazard has little to do with beanball by emphasizing the greater returns to throwing at an opposing team's star batter rather than at its pitcher and by reporting some data suggesting that National League pitchers are hit by pitches less often than other players are and, hence, tend not to be the targets of retaliation.

Inter-league differences in the composition of batters likewise provide the basis for Levitt's comment. Also relying on post-1990 data, he finds that only about 20% of the higher rate of hit batsmen in the American League can possibly be attributed to moral hazard. Levitt's conclusion rests on observations that pitchers are rarely punished for hitting an opposing batter and that "there does not appear to be any correlation between the frequency with which pitchers hit opposing batsmen and the likelihood that the pitcher will himself be hit while at the plate" (p. 687). As a matter of fact, when pitchers are excluded from the National League sample, there does not seem to be any difference between leagues in the rates at which batters are hit by pitches over the four seasons (19931996) for which Levitt reports data.

In sum, the DH effect identified in our original paper seems to weaken or disappear when years beyond 1990 are taken into account. As Table I of Trandel, White, and Klein clearly shows, the 1993 baseball season was a watershed in the time series of inter-league differences in hit batsmen. Beginning that year, the number of batters hit by pitches soared in both leagues-so much so in the National League that in three of the following seasons (1994, 1995, and 1997), the rate of hit batsmen there exceeded the corresponding AL rate for the first time since the mid 1960s (before the DH rule went into effect). What explains this apparent regime change? Neither comment addresses this important issue. Did the composition of batters in the NL shift significantly in 1993? Did NL batters suddenly become better hitters and, if so, why has this newfound prowess at the plate persisted, at least through the 1997 season? Such explanations seem implausible, but in any case unanswered questions such as these leave open the possibility that whatever events interrupted the patterns established during the previous 20 years have masked the DH rule's significance as a determinant of inter-league differences in hit batsmen beyond 1990.(3)

In any case, we have already tested the alternative hypothesis. Regression results reported in Table II of our 1997 paper explicitly controlled for the effects of inter-league differences in hitting and pitching performances. Specifically, we included observations on slugging averages, home runs, walks, strikeouts, saves, and game attendance (a proxy for pitchers' marginal returns to winning) as independent variables in a regression model run on data for 1921-1989. While only saves and game attendance were statistically significant, the DH rule's marginal impact on the excess number of batters hit by pitches in the American League was considerably larger than the 10% to 15% increase estimated with more parsimonious models similar to that of Trandel, White, and Klein. This evidence, which fails to support the contention that better hitting in the American League explains observed interleague differences in hit batsmen, is not mentioned in either comment.

We concede that the 1990s are different. The question is, why? Although the new data available to us define a time frame that is too brief to answer this question completely,(4) closer attention to events taking place in the National League suggests that an explanatory variable omitted by Trandel, White, and Klein has masked the true effects of the DH rule over the 1993-1997 period.

It is important to emphasize the magnitude of the regime change that occurred in 1993. Beginning that year, the number of batters hit by pitches increased dramatically in both leagues. But the increase in hit batsmen in the National League swamped the corresponding increase in the American League: from its 1992 value, the number of NL batters hit by pitches per 10,000 at-bats rose from 60 to 100. The jump in NL hit-batsmen rates from 1993 to 1997 amounts to an increase of 4.5 standard deviations based on summary statistics calculated for the 1947-1992 period. By way of contrast, the hit batsmen rate in the American League rose from 76 to 86 per 10,000 at-bats, an increase of about one standard deviation relative to the 1947-1992 period. Similar conclusions can be drawn by comparing 19931997 with either the prior five or ten years of data.

In short, the increase in the number of batters hit by pitches in the National League beginning in 1993 was unprecedented. And it is the unusually large increase in the NL hit batsmen series that masks the DH effect. This can be seen either by excluding the 1993-1997 period altogether or by explicitly controlling for it. Whether differences in levels or rates of hit batters are used as the dependent variable, regression estimates for 1947-1992 show that the estimated coefficient on the DH dummy variable is significant and that its effect is slightly larger than that reported for 1947-1990 by Trandel, White, and Klein.(5) When the full 1947-1997 period is examined and a dummy variable is included to control for the years 1993 through 1997, the DH effect also holds at the levels originally estimated by us.(6)

These new results indicate that the DH effect reported in our 1997 paper was not mere happenstance. Rather, the significance of the dummy variable controlling for 1993-1997 suggests the omission of an important exogenous event by Trandel, White, and Klein in estimating their updated version of our model. What exogenous event could have caused such an unusual increase in the National League hit batsmen series relative to the American League? The most obvious candidate was the expansion of the National League into Denver and Miami during the 1993 season. The expansion draft for these new franchises led to an influx of relatively inexperienced pitchers into the National League. Because of inter-league trading and free-agency, the effect would have spilled over into the American League, but unlikely to the same extent.

The other clearly identifiable event that occurred in the 1993-1997 time frame was the players' strike which cut short the 1994 season and curtailed spring training in 1995. One would expect the long-term impact of the labor dispute to be the same in both leagues. Yet, the realized effects of the strike may have caused the marginal benefits and marginal costs of throwing at opposing batters to differ systematically across leagues in the short run.

Lastly, both comments are silent on another key element of the empirical evidence we reported demonstrating the DH rule's effect on hit batsmen, namely the long-run time series data. Table Ill in our 1997 paper presents Johansen cointegration tests for the American and National League over 1901-1972 and 1901-1990, rejecting the null hypothesis of no cointegration over the pre-DH era but failing to reject it when years beyond 1973 were included. Because this kind of evidence is not as sensitive to short run, atypical variability in the series, we direct attention back to it using the extended sample period, 1901-1997, and using differences in levels as well as rates of hit batsmen.

Consistent with the results in our earlier paper, the null hypothesis of no cointegration is rejected at the 5% level for both differences in levels and differences in rates. However, the null is not rejected for either series when the sample includes 1973--1997.(7) Even when the aberrant 1993-1997 period is included, a fundamental difference in the time series before and after 1972 can be detected.

As an addendum to the cointegration tests, we also estimated error correction models for the American League hit batter data both in levels and in rates. The error correction approach allows for the long-run relationship between American and National League hit batsmen to be estimated (rather than imposing a restrictive relationship by differencing), while also estimating the effects of the introduction of the DH rule. We utilize the "long version" of error correction modeling as explained in Mehra [1992]. Equations (1) and (2) below show the results (t-statistics in parentheses):

(1) [Mathematical Expression Omitted]

(2) [Mathematical Expression Omitted]

In both of these equations, the DH coefficient is positive and significant at the 5% level.(8) The magnitude of the effect in equation (2) is about the same as in the earlier results, while the effect in equation (1) is diminished.

III. CONCLUDING REMARKS

The comments sparked by Goff, Shughart, and Tollison [1997] demonstrate that, despite strikes, free agency, and league expansion, a significant number of economists still maintain a residual interest in the game of baseball. We share that interest. Baseball supplies a natural experimental laboratory for testing bedrock economic theories about how changes in the rules of the game affect human behavior. The empirical results we reported earlier lent support to the hypothesis that American League pitchers became much more willing to throw at opposing batters after the DH rule went into effect in 1973. Taking the new evidence adduced by the commentators on our paper at face value requires us to concede that events in the 1990s produced changes in the time series of inter-league differences in hit batsmen that may or may not fit the moral hazard hypothesis. But they surely do not fit the alternative hypothesis that time-wise variations in the frequency with which batters are hit by pitches can be explained by time-wise variations in batting skills. Neither does the new evidence obviate the fact that the DH effect we identified persisted for at least 20 years. We did not assert that moral hazard was capable of explaining all of the inter-league differences in hit batsmen for all time, but only that, by changing the constraints facing American League pitchers, at the margin and other things being equal, the introduction of the DH rule allowed them to throw at opposing hitters with greater impunity (i.e., at a lower cost) than National League pitchers, who still must take their turns at bat.

1. This estimate is based on a regression specification which uses inter-league differences in hit batsmen rates (per 10,000 at-bats) as the dependent variable. Trandel, White, and Klein's alternative specification allows the number of hit batsmen to be proportional to the number of at-bats rather than being restricted to the constant function modeled in our 1997 paper. The estimated coefficient on the DH dummy variable loses its statistical significance when the additional observations are included in Trandel, White, and Klein's rate-difference equation and, while the estimated coefficient remains significant in the levels-difference equation estimated by us, the designated hitter rule is responsible for elevating the number of batters hit by pitches in the American League by only about 3% over the 1947-1997 period.

2. This is equivalent to arguing that there is worse pitching in the American League, a consideration supported by data supplied to us in a personal communication by Allen Sanderson, who states that more runs are scored per game in the American League than in the National League, on the average, and, hence, that AL pitchers have higher ERAs (earned-run averages) than their NL counterparts. We thank Sanderson for bringing this to our attention.

3. It is also worth emphasizing that moral hazard is not ruled out by data showing that pitchers themselves are not frequently the targets of retaliation when they hit opposing batters. If, as we argued in our 1997 paper, the DH rule affected pitchers' marginal decision-making calculus, then it is at the margin where the predicted effects are to be found. Comparing totals to totals is not the right test.

4. In what follows, we report results based on data through the end of the 1997 regular baseball season, which Greg Trandel graciously provided to us.

5. For 1947-1992 inter-league differences in hit batsmen levels with at-bats as an independent variable, the DH coefficient is 45.13 with a t-statistic of 4.25. For 1947-1992 inter-league differences in hit batsmen rates, the DH coefficient is 7.67 with a t-statistic of 3.00. Both models include corrections for first-order serial correlation.

6. For 1947-1997 inter-league differences in hit batsmen levels with at-bats and a dummy for 1993-1997 as independent variables, the DH coefficient is 43.58 with a t-statistic of 2.11. For 1947-1997 inter-league differences in hit batsmen rates with a dummy for 1993-1997 as an independent variable, the DH coefficient is 7.67 with a t-statistic of 3.00.

7. For the differences in levels, the likelihood ratio for 1901-1972 is 16.4, and it is 5.01 for 1901-1997. For differences in rates, the likelihood ratio for 1901-1972 is 24.77, and it is 14.40 for 1901-1997. The critical value ([Alpha] = .05) for rejecting the null hypothesis of no cointegration is 15.41.

8. The coefficient of multiple determination for equation (1) is 0.16; it is 0.10 for equation (2). Box-Pierce Q(12) statistics do not reject the null hypothesis of no serial correlation.

REFERENCES

Goff, Brian L., William F. Shughart II and Robert D. Tollison. "Batter Up! Moral Hazard and the Effects of the Designated Hitter Rule on Hit Batsmen." Economic Inquiry, July 1997, 555-61.

Levitt, Stephen D. "The Hazards of Moral Hazard: Comment on Goff, Shughart, and Tollison." Economic Inquiry, October 1998, 685-87.

Mehra, Yash P. "In Search of a Stable, Short-Run M I Demand Function." Federal Reserve Bank of Cleveland Economic Review, May-June 1992, 9-23.

Trandel, Gregory A., Lawrence H. White and Peter G. Klein. "The Effect of the Designated Hitter Rule on Hit Batsmen: Pitcher's Moral Hazard or the Team's Cost-Benefit Calculation? A Comment." Economic Inquiry, October 1998, 679-84.