The regional distribution of bank closings in the United States from 1982 to 1988: a brief note.I. Introduction In an earlier article in this Journal, Amos [1] presents a crosssection cross section also crosssec·tion n. 1. a. A section formed by a plane cutting through an object, usually at right angles to an axis. b. A piece so cut or a graphic representation of such a piece. 2. analysis to explain the regional distribution of bank closures. While he presents a strong case for the importance of regional economic factors and state branching regulations in explaining the percentage of bank failures from 198288, Amos finds statistical significance for only a few of the independent variables in his model. I believe that Amos's inability to find statistical significance is caused by the regression regression, in psychology: see defense mechanism. regression In statistics, a process for determining a line or curve that best represents the general trend of a data set. technique that he employs. Amos uses ordinary least squares (OLS OLS Ordinary Least Squares OLS Online Library System OLS Ottawa Linux Symposium OLS Operation Lifeline Sudan OLS Operational Linescan System OLS Online Service OLS Organizational Leadership and Supervision OLS On Line Support OLS Online System ) to estimate the percentage of bank failures. However, ten states experienced no bank failures from 198288. Thus, there is a significant number of observations where the dependent variable is truncated truncated adjective Shortened at zero. The appropriate estimation estimation In mathematics, use of a function or formula to derive a solution or make a prediction. Unlike approximation, it has precise connotations. In statistics, for example, it connotes the careful selection and testing of a function called an estimator. technique for a distribution with this characteristic is Tobit Tobit (tō`bĭt) [Gr. from Heb. Tobijah="God is my good"], book of the Old Testament Apocrypha, not included in the Hebrew Bible. It is the account of Tobit, a devout Jew in exile, and of his son Tobias. [2, 682690]. The purpose of this comment is to reestimate Amos's model using the correct estimation technique, Tobit, as well as to correct the estimates for heteroscedasticity heteroscedasticity an irregular scattering of values in a series of distributions; accompanied by a comparable scatter of variances. . II. Model and Regression Results Based on his analysis of the historical trend in bank closings from 1934 to 1988, Amos argues that the level of production activity within a state, as measured by gross state product, will affect the number of bank closures. He hypothesizes that healthy state economies will have a lower level of bank closures. Thus, he predicts a negative relationship between the percentage of bank closures and gross state product. Amos also argues that regional economic factors affect the percentage of bank closures. He observes that two of the nine census regions, West South Central and West North Central, contain over half of the bank closings from 198288. However, the New England New England, name applied to the region comprising six states of the NE United States—Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and Connecticut. The region is thought to have been so named by Capt. , MidAtlantic Adj. 1. midAtlantic  of a region of the United States generally including Delaware; Maryland; Virginia; and usually New York; Pennsylvania; New Jersey; "midAtlantic states" middle Atlantic , and South Atlantic regions had less than five percent of the total bank closures during this period. In the remaining regions, East North Central, East South Central, Mountain, and West, the majority of the bank closures were concentrated in one or two states within each region. Amos attributes this regional variation in the distribution of bank closures to the differences in the core economic activity in each region. He observes that the ten states with the highest shares of gross state product from oil and gas extraction have fiftyfour percent of the bank closures, that the top ten farming states have twentytwo percent of the bank closures, and that the top ten states with the greatest proportion of gross state product coming from manufacturing have only two percent of the bank closures from 198288. Thus, Amos believes that the percentage of gross state product generated from oil and gas extraction and the percentage of gross state product generated from agriculture will be positively related to the percentage of bank failures while the percentage of gross state product generated from manufacturing will be negatively related to the percentage of bank failures. Amos also hypothesizes that differences in state branching regulations will affect the percentage of bank failures. Amos observes that over half of the bank failures during the period 198288 occurred in states characterized char·ac·ter·ize tr.v. character·ized, character·iz·ing, character·iz·es 1. To describe the qualities or peculiarities of: characterized the warden as ruthless. 2. by unit branching in 1980 and that nine of the ten states experiencing no bank closures during this period had statewide branching regulations in effect in 1980. Thus, Amos expects a positive relationship between the percentage of bank failures and the existence of unit branching regulations within a state in 1980 and a negative relationship between the percentage of bank failures and the existence of statewide branching regulations within a state in 1980. The last three variables, GAR gar, member of the family Lepisosteidae, freshwater fishes found in the warmer rivers and lakes of the S United States, Central America, Mexico, and the West Indies. Gars are highly predacious and destroy many useful fish. , the average annual growth rate of gross state product from 1963 to 1986; GDR GDR See Global Depositary Receipt (GDR). , the difference between the average rate of growth of gross state product in the late 1970s and the early 1980s; and GVR GVR Grant, Vacate and Remand GVR Gas Volume Ratio , the variance The discrepancy between what a party to a lawsuit alleges will be proved in pleadings and what the party actually proves at trial. In Zoning law, an official permit to use property in a manner that departs from the way in which other property in the same locality of annual rates of growth of gross state product for the period 1963 to 1986; test for instability instability /in·sta·bil·i·ty/ (stahbil´ite) lack of steadiness or stability. detrusor instability in the state's economies. Amos uses GAR to indicate whether faster or slower growing states experience a higher percentage of bank failures; GDR indicates whether a change in the rate of growth between the late 1970s and the early 1980s affected the percentage of bank failures, and GVR indicates if states with historically more volatile growth rates Growth Rates The compounded annualized rate of growth of a company's revenues, earnings, dividends, or other figures. Notes: Remember, historically high growth rates don't always mean a high rate of growth looking into the future. experienced more volatility in their banking industry. Amos does not indicate whether he expects a positive or a negative relationship to exist between the last three variables discussed and the percentage of bank failures. Table I presents the results obtained from the OLS and Tobit regressions. Column 1 presents Amos's original results using ordinary least squares and Column 2 presents the results obtained using Tobit analysis. Given the nature of Amos's data, heteroscedasticity may be a problem; thus, the Tobit results reported are corrected for heteroscedasticity. The variables used to explain the percentage of bank failures are defined as follows: GSP GSP Good Scientific Practice GSP Generalized System of Preferences GSP Gross State Product GSP German Shorthaired Pointer (dog breed) GSP Geometer's Sketchpad (KTP Technologies geometry software) GSP Georges St. is gross state product in 1980; DMUN is a dummy variable This article is not about "dummy variables" as that term is usually understood in mathematics. See free variables and bound variables. In regression analysis, a dummy variable that takes the value 1 if the state has unit branching regulations in effect in 1980 and zero otherwise; DMST DMST Do Make Say Think (band) DMST Department of Management Science and Technology DMST Demonstrate DMST Department of Military Science and Tactics DMST Danish Mental Status Test DMST Directed Minimal Spanning Tree is a dummy variable that takes the value 1 if a state has statewide branching regulations in effect in 1980 and zero otherwise; AGP (Accelerated Graphics Port) A highspeed 32bit port from Intel for attaching a display adapter to a PC. It provides a direct connection between the card and memory, and only one AGP slot is on the motherboard. is the percentage of gross state product generated from agriculture in 1980; EGP (1) (Exterior Gateway Protocol) A broad category of routing protocols that are designed to span different autonomous systems. Contrast with IGP. (2) (Exterior Gateway P is the percentage of gross state product generated from oil and gas extraction in 1980; MGP (Monochrome Graphics Printer port) A display adapter that employs Hercules Graphics and a parallel printer port on the same expansion board. is the percentage of gross state product generated from manufacturing in 1980; GAR is the average annual growth rate of gross state product from 1963 to 1986; GDR is the difference between the average annual growth rates of gross state product for 19751980 and 198085; GVR is the variance of annual rates of growth of gross state product for the period 1963 to 1986. The OLS results support some of Amos's hypotheses. The percentage of bank failures is significantly related to the size of the state's economy (GSP), but the sign of the variable is positive, not negative. The percentage of gross state product generated from oil and gas extraction (EGP) and the volatility of the state's economy (GVR) are both positively and significantly related to the percentage of bank failures from 198288. Amos predicts the positive and significant sign for EGP, and he hypothesizes that GVR will affect the percentage of bank closures, but he does not indicate whether GVR will have a positive or a negative relationship with the percentage of bank closures. Amos also finds that states with a relatively higher average growth rate in the early 1980s than the late 1970s (GDR) have a lower percentage of bank closures. Again, Amos expects some significance for this variable, but he does not indicate the direction of the relationship between this variable and the percentage of bank failures. However, according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. Amos's OLS results, neither state branch banking regulations (DMUN and DMST) nor the percentage of gross state product generated from either agriculture (AGP) or manufacturing (MGP) are related to the percentage of bank failures.(1) Table I. Regression Results (tstatistics in parentheses) Independent Variable Ordinary Least Squares Tobit Constant 0.045 0.025 (1.07) (1.67)(*) GSP 0.3E3 0.392 (2.48)(**) (11.68)(**) DMUN 0.027 0.032 (1.33) (1.16) DMST 0.020 0.019 (1.22) (2.39)(**) AGP 0.002 0.695 (0.66) (4.29)(**) EGP 0.003 0.338 (2.64)(**) (2.39)(**) MGP 0.002 0.132 (0.24) (3.23)(**) GAR 0.007 1.466 (0.88) (1.54) GDR 0.008 1.001 (2.12)(**) (2.65)(**) GVR 0.003 51.109 (2.56)(**) (2.15)(**) [R.sup.2] = .60 Loglikelihood ratio = 125.4(**) F(9, 41) = 9.275(**) Limit Observation = 10 N = 50 N = 50 ** Significant at 95% level * Significant at 90% level The Tobit model The Tobit Model is an econometric, biometric model proposed by James Tobin (1958) to describe the relationship between a nonnegative dependent variable , corrected for heteroscedasticity, yields different regression results. The percentage of bank failures is still positively and significantly related to gross state product (GSP), the percentage of gross state product generated from oil and gas extraction (EGP), and the variance in the growth rate of gross state product (GVR), but gross state product is much more significant in this model than the OLS model. In addition, the percentage of gross state product generated from agriculture (AGP) is positively and significantly related to the percentage of bank failures as is the dummy variable capturing the effects of statewide branching regulations (DMST). The variance in growth rates is still negative and statistically significant, but so is the percentage of gross state product generated from manufacturing (MGP). State branch banking regulations are significant in this model; states with statewide branching have a higher percentage of bank failures, ceteris paribus Ceteris Paribus Latin phrase that translates approximately to "holding other things constant" and is usually rendered in English as "all other things being equal". In economics and finance, the term is used as a shorthand for indicating the effect of one economic variable on . However, the sign of this variable is the opposite of what Amos expects, and the dummy variable that captures the effect of unit branching regulations (DMUN) is insignificant. The constant, which captures the effects of limitedbranching regulations is negative and significant in the Tobit regression, indicating that states with limitedbranching regulations had a lower percentage of bank closures. Thus, the use of Tobit analysis, corrected for heteroscedasticity, provides much stronger support for Amos's model. Gross state product (GSP) is significantly related to the percentage of bank failures, but it has a positive rather than a negative sign. The variables capturing differences in the individual state's economic base, the percentage of gross state product generated from oil and gas extraction (EGP), the percentage of gross state product generated from agriculture (AGP), and the percentage of gross state product generated from manufacturing (MGP), are each significant and have the expected sign. State branching regulations, as indicated by the significance of the constant, which captures the effect of limitedbranching regulations, and the dummy variable for statewide branching, also affect the percentage of bank failures. III. Conclusions Amos hypothesizes that both branch banking regulations and regional economic factors affect the distribution of bank failures from 198288. Using ordinary least squares regression, he finds some support for his hypothesis. States with larger, more volatile economies, dependent on the oil industry, with higher growth rates in the early 1980s than the late 1970s have a higher percentage of bank failures. However, ordinary least squares is not the appropriate estimation technique when there is a significant number of observations truncated at zero. Reestimating Amos's model using the appropriate estimation technique, I find much stronger support for his hypothesis. States with larger, more volatile economies, dependent on either energy production or farming were more likely to experience bank failures. States dependent on manufacturing had a lower percentage of bank failures. States characterized by statewide branching had a higher percentage of bank failures, and states with limitedbranching regulations had a lower percentage of bank failures. 1. The Tobit model estimated without the heteroscedasticity correction gives results similar to the OLS model. References 1. Amos, Orley M., Jr., "The Regional Distribution of Bank Closings in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. from 1982 to 1988." Southern Economic Journal, January 1992, 80515. 2. Greene, William H. Econometric e·con·o·met·rics n. (used with a sing. verb) Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models. Analysis. New York New York, state, United States New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of : MacMillan Publishing Company, 1993, pp. 68290. 

Reader Opinion