The Federal Reserve Bank has estimated the following two alternative models for the number of banks in the USA that declare default each year, as follows:

Model 1
Default = 12.25 – 0.09*X1 + 0.04*X2 + 0.14*X3 – 0.05*X4 + 0.01*X5

R-squared 0.88 and DW statistic 0.35

Model 2
Δ(Default) = 2.7 – 0.003*Δ(X1) + 0.002*Δ(X2) + 0.09*(X3) – 0.01*Δ(X4) + 0.002*Δ(X5)

R-squared 0.43 and DW statistic 1.99
Where
Default is the number of banks that have declared default
X1: is the annual US GDP per capita
X2: is the US unemployment rate
X3: is a variable attaining the value 1 if in a given year there is a financial crises and zero otherwise
X4: is the logarithm of the value of total liquid reserves held by the US banking sector
X5: is the product of X2 and X3

• Show what the DW statistics imply for the correlation of the error terms in each of the regressions. Also, discuss what these correlations imply for the effect of shocks across time
• Which of the two model specifications should the researcher adopt, and why?
• Discuss the qualitative and quantitative impact of the occurrence of crises on the number of bank defaults
• Discuss the impact of unemployment rate on the number of bank defaults