Estimate A Regression Of Ln(vio) Against Shall, Incarcrate ✓ Solved

Estimate a regression of ln(vio) against shall, incarc_rate

Please use the attached 3 files to complete the assignment. You need to submit the syntax file and output file for SPSS software. In the Guns dataset uploaded with this HW, there is data for 50 US states and the District of Columbia for twenty years.

1. Estimate a regression of ln(vio) against shall, incarc_rate, density, avginc, pop, pb1064, pw1064 and pm1029. Use HC1 standard errors. The regression model should have an intercept.

2. Add in state fixed effects to the regression in Q1. Use HC1. Do not include an intercept in this regression.

3. Add in time fixed effects to the regression in Q1. Use HC1. Do not include an intercept in this regression.

4. Add in both state and time fixed effects to the regression in Q1. Use HC1. Do not include an intercept in this regression.

5. Examine the results from the 4 models you’ve estimated. Comment specifically on the coefficient on shall. Does the magnitude or sign or significance of the variable change as you add in state, time, or both state and time fixed effects? You can use a 5% level of significance to compare, if needed.

Paper For Above Instructions

The study of gun violence and its relation to various factors such as legislation, incarceration rates, and population density is complex and requires an in-depth analysis using powerful statistical methods. In this paper, we will conduct a regression analysis on the Gun dataset which comprises information from 50 U.S. states and the District of Columbia over a period of twenty years. The primary objective is to estimate the regression of the natural logarithm of violent crime rate (ln(vio)) against several independent variables: shall, incarc_rate, density, avginc, pop, pb1064, pw1064, and pm1029. The analysis will be performed using SPSS software, and results will be interpreted based on the specifics of each regression model estimated.

### Model 1: Basic Regression with HC1 Standard Errors

The first step in our analysis involves estimating a regression model which includes an intercept. The dependent variable, ln(vio), represents the natural logarithm of violent crime rates, while the independent variables will include shall (the extent of carry laws), incarceration rates, population density, average income, total population, and specific demographic indicators (pb1064, pw1064, and pm1029). The HC1 standard errors will be used to account for heteroskedasticity.

Upon running the regression with SPSS, the output will show the coefficients, standard errors, t-statistics, and p-values for each of the variables. Special attention will be paid to the shall variable to observe its initial impact on violent crime rates.

### Model 2: Adding State Fixed Effects

The second model will incorporate state fixed effects. In regression analysis, including fixed effects allows us to control for unobserved characteristics of states that do not change over time. In this model, we will omit the intercept, as specified in the assignment. The output at this stage will provide insights into how fixed state characteristics influence our primary variable of interest, particularly examining any changes in the coefficient of shall.

### Model 3: Introducing Time Fixed Effects

Next, the analysis will expand to include time fixed effects. This model will also not contain an intercept. By adding time fixed effects, we can account for unobservable factors that are constant across states but may vary over time, such as national trends in crime rates. We will analyze the results to identify changes in the shall coefficient once these time effects are taken into consideration.

### Model 4: Combining State and Time Fixed Effects

The final model will merge both state and time fixed effects, once again excluding the intercept. This comprehensive model will allow us to adjust for both fixed characteristics of states and temporal dynamics. Analyzing the outputs from this model will provide a holistic view of the relationships between the independent variables and the violent crime rate and how they might be influenced by simultaneous state and temporal effects.

### Results Evaluation

After estimating all four models, we will closely examine the coefficients of the shall variable across the different model specifications. It is crucial to analyze any variations in the magnitude, sign, or significance of the shall coefficient as we add more fixed effects into the model. This evaluation will highlight the robustness of the shall law's effects on violent crime rates and offer insights based on the statistical significance at a 5% level.

Commenting on the shall coefficient will allow us to assess whether it has become more significant with fixed effects, suggesting that accounting for state and time specificities may either obscure or enhance its perceived impact on violence rates. We can summarize our findings with details regarding whether legislative influences stand strong amidst the control variables or whether they falter under closer scrutiny with fixed effects included.

References

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