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 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 technique that he employs. Amos uses ordinary least squares (OLS) 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 at zero. The appropriate estimation technique for a distribution with this characteristic is Tobit [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. 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, MidAtlantic, 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 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, the average annual growth rate of gross state product from 1963 to 1986; GDR, the difference between the average rate of growth of gross state product in the late 1970s and the early 1980s; and GVR, the variance of annual rates of growth of gross state product for the period 1963 to 1986; test for 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 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 is gross state product in 1980; DMUN is a dummy variable that takes the value 1 if the state has unit branching regulations in effect in 1980 and zero otherwise; DMST is a dummy variable that takes the value 1 if a state has statewide branching regulations in effect in 1980 and zero otherwise; AGP is the percentage of gross state product generated from agriculture in 1980; EGP is the percentage of gross state product generated from oil and gas extraction in 1980; MGP 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 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, 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. 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 from 1982 to 1988." Southern Economic Journal, January 1992, 80515. 2. Greene, William H. Econometric Analysis. New York: MacMillan Publishing Company, 1993, pp. 68290. 

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