#1. Provide a table of summary statistics for this data.


United States Phillips Curve Data Set, monthly (1950-2021)

3 Variables   862 Observations
wage
image
nmissingdistinctInfoMeanGmd.05.10.25.50.75.90.95
68218066714.1682.1171.9342.1912.6313.6855.6567.4337.911
lowest : 1.15262 1.17587 1.38675 1.39104 1.39752 , highest: 8.96861 9.02367 9.04977 9.07738 9.28463
cpi
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        n  missing distinct     Info     Mean      Gmd      .05      .10      .25 
      862        0      846        1    3.464    2.895   0.2265   0.9098   1.6340 
      .50      .75      .90      .95 
   2.8314   4.3543   6.9092  10.0652
lowest : -2.08247 -1.95876 -1.48384 -1.37794 -1.25471 , highest: 14.16185 14.26593 14.42577 14.58924 14.59227
unrate
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nmissingdistinctInfoMeanGmd.05.10.25.50.75.90.95
8620830.9995.7891.8743.53.84.65.66.98.09.1
lowest : 2.5 2.6 2.7 2.8 2.9 , highest: 10.4 10.8 11.1 13.3 14.8



#2. Provide a plot for the price inflation and wage inflation data series. Explain what you see. What can you say about both of these data series?



United States Cost of Goods and Wage Inflation as a Percent (1950-2020)

During the 1960s to the 1980, in the United States we saw a continuous rise in prices and inflation. This makes sense due to the rise in the price level due to the reduction in the buying in the value of the dollar. Following 1981 it is apparent that we see a rapid decrease in the level of inflation. This decrease in inflationary pressures was caused by the United States working to collect on sovereign debts then making domestic buying power increase due to the reduction in the aggregate money supply. Following this reduction in inflationary pressure the United States enters a period of fifteen years of a relatively consistent and cyclical increases and decreases in inflation. In the 2008 financial crisis we see an inversely reaction to the cost of goods and inflation. This makes logical sense due to the loss of aggregate money supply we would see a reduction in the price level. Recently in 2020 COVID has caused both of these charts to increase rapidly due to the monetary stimulus that has been injected in the economy.



3. Estimate a baseline Phillips curve using U.S. data for both price inflation and wage inflation. Provide a summary table of residuals from both models. What can you conclude from this table?

The Inverse Relationship Between Unemployment and Inflation
Dependent variable:
Percent Change in Unemployment
(1) (2)
1% increase in CPI -0.520***
(0.140)
1% increase in Wage -0.228
(0.178)
Constant 5.793*** 6.023***
(0.058) (0.066)
Observations 861 681
R2 0.016 0.002
Adjusted R2 0.015 0.001
Residual Std. Error 1.689 (df = 859) 1.731 (df = 679)
F Statistic 13.786*** (df = 1; 859) 1.644 (df = 1; 679)
Note: p<0.1; p<0.05; p<0.01


OLS Anaylsis

What I can conclude from these models is there is a inverse relationship between the unemployment rate and inflation. When looking at the relationship between the consumer price index and unemployment it is significant at a 99% confidence interval. Although the wage inflation does not have near as strong of a inverse relationship with the unemployment rate.



4. Plot the residuals as a time series. Identify the periods of time that the model does not fit well.




5. Using the plot function, provide a plot of Cook’s Distance for both regressions. Are the outliers from the plot different from what you observe in (4)? Explain.

Cook’s Distance of datasets

These plots show a lot of what I see with the plots on number four. Cook’s Distance does a better job of showing the standalone data points that skew the data set. In the second plot the data point that is a large outlier and would be a cause for concern and might need to be checked the validity of the data. Leading into problem number six it is imperative to use the information that cook’s distance has providing in understanding what windows might be best for our models.



6. Use the algorithm we used in class to test the stability of the parameterestimates for both models. Define the windows you are testing. Why did you pick them? Justify your choice.

The Inverse Relationship Between Unemployment and Inflation,
Dependent variable:
Percent Change in Unemployment
(1) (2)
1% increase in CPI -1.319***
(0.192)
1% increase in Wage -0.695**
(0.270)
Constant 6.058*** 6.388***
(0.064) (0.076)
Observations 487 356
R2 0.089 0.018
Adjusted R2 0.087 0.016
Residual Std. Error 1.402 (df = 485) 1.429 (df = 354)
F Statistic 47.216*** (df = 1; 485) 6.638** (df = 1; 354)
Note: p<0.1; p<0.05; p<0.01


OLS Anaylsis

I have had issues with ts conversion, but using the basis over the length over observation it has seeming strengthen the model. This is caused by the outliers being removed from the data, these outliers were data points in which intervention into the economy had taken place. This inference could be incorrect if it the relationship changed after the intervention into the economy.



7. Summarize the results in some way. What do you conclude?

Summarizing the problem set it shows us that there still exist a inverse relationship within the the unemployment rate and the inflation.