ECON5403 Econometric Theory and Methods : Several Variables
1.Are longer prison sentences likely to reduce the incidence of crime?
2.Are policies that increase the probability of arrest (e.g. more police patrols) likely to reduce the incidence of crime?
3.Are higher employment rates likely to reduce the incidence of crime?
4.Are improved income support schemes (e.g. higher social security payments) likely to reduce the incidence of crime?
Answer:
Introduction
Econometric techniques are evaluation tools that employ mathematical and statistical associations to model the economy (Diebold, 2018). Econometric techniques normally employ large quantities of data and several variables. There are two common econometric techniques: least square regression analysis (i.e. OLS method), and time-series analysis. Least square regression analysis tries to establish a causation relationship between the independent (predictor) variable, and dependent (response) variable (Kacapyr, 2014). On the other hand, a time-series analysis relies on patterns in the data to make forecasts about future expectations e.g. the interest rate in 2020.
Are longer prison sentences likely to reduce the incidence of crime?
justify;">We will use OLS (Ordinary Least Square) method for this problem the independent variable will be the number of crimes in 1986 and the dependent variable will be the months in prison during 1986. This econometric technique is appropriate because it helps affirm association between to variables. The analysis seeks to prove that when the individuals are given longer prison sentences there are lesser crime reports. The naive assumption is that the criminals spend a majority of their year (1986) behind bars as such they have few opportunities to commit crime. The other assumption is that the individuals shy away from criminal activities after they are released from prison in order to avoid extended prison visits in future. After Running the OLS analysis we are able to get the following results. The equation below indicates that an increment in prison sentence does reduce the prevalence/incidence of crime.
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^arr86 = 0.283 - 0.0132*ptime86 (0.00878)(0.00440) n = 2700, R-squared = 0.003 (standard errors in parentheses) |
The results below indicate that the OLS model is not significant at alpha= 0.05. Likewise the constant and independent variable are also not significant at a 5% significance level. It is also important to note that the R-squared is considerably small indicating that a very small change in the dependent variable can actually be explained by the independent variable. The test for heteroskedasticity showed that we will reject the null hypothesis (Ho: heteroskedasticity not present). Therefore, we can conclude that variability in the dependent variable is unequal across the values of the predictor variable. This model is therefore not the most appropriate to use.
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Model 2: OLS, using observations 1-2700 Dependent variable: arr86 coefficient std. error t-ratio p-value --------------------------------------------------------- const 0.282932 0.00877727 32.23 3.93e-193 *** ptime86 −0.0132417 0.00439863 −3.010 0.0026 *** Mean dependent var 0.277778 S.D. dependent var 0.447986 Sum squared resid 539.8533 S.E. of regression 0.447319 R-squared 0.003348 Adjusted R-squared 0.002978 F(1, 2698) 9.062649 P-value(F) 0.002633 Log-likelihood −1658.026 Akaike criterion 3320.052 Schwarz criterion 3331.854 Hannan-Quinn 3324.320 White's test for heteroskedasticity - Null hypothesis: heteroskedasticity not present Test statistic: LM = 125.322 with p-value = P(Chi-square(2) > 125.322) = 6.11923e-028 |
Are policies that increase the probability of arrest (e.g. more police patrols) likely to reduce the incidence of crime?
Yes, from the results below the increment in police patrols will lower the crime incidences; in spite of the lack of significance with regard to the two independent variable and well as the model itself.
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^arr86 = 0.338 - 0.169*pcnv (0.0115)(0.0216) n = 2700, R-squared = 0.022 (standard errors in parentheses) |
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Model 3: OLS, using observations 1-2700 Dependent variable: arr86 coefficient std. error t-ratio p-value --------------------------------------------------------- const 0.338178 0.0115102 29.38 7.28e-165 *** pcnv −0.168551 0.0215747 −7.812 7.97e-015 *** Mean dependent var 0.277778 S.D. dependent var 0.447986 Sum squared resid 529.6842 S.E. of regression 0.443085 R-squared 0.022121 Adjusted R-squared 0.021759 F(1, 2698) 61.03394 P-value(F) 7.97e-15 Log-likelihood −1632.354 Akaike criterion 3268.708 Schwarz criterion 3280.510 Hannan-Quinn 3272.976 |
Are higher employment rates likely to reduce the incidence of crime?
Yes, from the results below the higher the employment rate the lower the crime incidences; in spite of the lack of significance with regard to the two independent variable and well as the model itself.
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^arr86 = 0.326 + 0.00637*durat - 0.0271*qemp86 (0.0189)(0.00212) (0.00607) n = 2700, R-squared = 0.020 (standard errors in parentheses) |
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Model 4: OLS, using observations 1-2700 Dependent variable: arr86 coefficient std. error t-ratio p-value --------------------------------------------------------- const 0.326133 0.0189094 17.25 2.59e-063 *** durat 0.00637031 0.00211735 3.009 0.0026 *** qemp86 −0.0271087 0.00606792 −4.468 8.24e-06 *** Mean dependent var 0.277778 S.D. dependent var 0.447986 Sum squared resid 530.8414 S.E. of regression 0.443651 R-squared 0.019985 Adjusted R-squared 0.019258 F(2, 2697) 27.49943 P-value(F) 1.50e-12 Log-likelihood −1635.300 Akaike criterion 3276.600 Schwarz criterion 3294.303 Hannan-Quinn 3283.002 |
Are improved income support schemes (e.g. higher social security payments) likely to reduce the incidence of crime?
No, from the results below the higher social security payments will cultivate higher crime incidences; in spite of the lack of significance with regard to the two independent variable and well as the model itself.
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^arr86 = 0.346 - 0.00124*inc86 (0.0110)(0.000127) n = 2700, R-squared = 0.034 (standard errors in parentheses) |
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Model 5: OLS, using observations 1-2700 Dependent variable: arr86 coefficient std. error t-ratio p-value ---------------------------------------------------------- const 0.346303 0.0109895 31.51 7.36e-186 *** inc86 −0.00124493 0.000127126 −9.793 2.83e-022 *** Mean dependent var 0.277778 S.D. dependent var 0.447986 Sum squared resid 523.0739 S.E. of regression 0.440312 R-squared 0.034325 Adjusted R-squared 0.033967 F(1, 2698) 95.90075 P-value(F) 2.83e-22 Log-likelihood −1615.400 Akaike criterion 3234.801 Schwarz criterion 3246.603 Hannan-Quinn 3239.069 |
Conclusion
It is important to note that changes in the data of one variable cannot always be predicted by the changes in the data of another variable. As such, it is very common to see that a particular OLS model predicts a positive relationship between to variables, but the model itself has no significance. Furthermore it is not uncommon for variations in the dependent variable's data to be totally unequivocal to that of the predictor variable. OLS models are therefore, great for predicting data that is void of extremes (outliners); meaning that some values are not too large or too small. In our above assessments; some of the variables accessed either had very large or very small values e.g. $140 and $0.
References
Diebold, F. (2018). Econometric Data Science. Penn Arts and Sciences , 23-34.
Kacapyr, E. (2014). A Guide to Basic Econometric Techniques. Armonk, NY: M.E. Sharpe.
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