2 (15 points) We want to analy;sumption in the US as anIntord function for both| Figure 2: Case-Shiller housing price index0=300134XXXXXXXXXX20 the Case-Shiller Housing price index...

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2 (15 points) We want to analy; sumption in the US as an Intord function for both | Figure 2: Case-Shiller housing price index 0=300134 800.4489 20 the Case-Shiller Housing price index using Food Cone. explanatory variable. Figure 2 and Figure 3 represent the 3 time series. Now, answer the sub-questions of 2(a) to 2(e). ACE for level I | i i (21 points + 3 bonus points) We want. to estimate the Cobb-Douglas production function for the US economy between 1961 and 2016 (T—56 years). The ble Y represents the total US GDP (trillion USD), K is capital, and L is labor. In order to estimate the production function using OLS, we use the following log-log model: n(Y:) = Bo + Buln(Ly) + aln(Ko) + uy. (1) Estimation results are presented in Figure 1. Note that LNY= log(GDP), LNL= log (labor), LNK= log(capital) - Figure 1: OLS estimates call: Im(formula = LNY ~ LNL + LNK) Residuals: Min 1Q Median .3qQ Max -0.39883 -0.14663 -0.02935 0.14349 0. 53839 Coefficients: Estimate std. Error t value Pr>it]) (Intercept) 1.72017 0.04855 35.43 <2e-16 "w="LNL" 0.39972="" 0.02939="" 13.60=""><2e-16 *#%="" lnk="" 0.41376="" 0.02589="" 15.98=""><2e-16 “a+="" signif.="" codes:="" 0="" ‘*="#'" 0.001="" ‘+!="" 0.01="" *'="" 0.05="" t.="" "io="" q)="" «ix="" residual="" standard="" error:="" 0.2038="" on="" 53="" degrees="" of="" freedom="" multiple="" r-squared:="" 0.8971,="" adjusted="" r-squared:="" 0.8932="" f-statistic:="" 230.9="" on="" 2="" and="" 53="" pf,="" p-value:=""><2. 20-16="" adf="" test="" &="" critical="" values="" v="" a="" 0%="" sms="" hf="" |="" 28="" 2s7="" 2p="" aes="" il="" ct="" a="" )="" oe="" kl="" vie="" (e)="" estimat="" il="" i="" prone="" wl="" in="" (i="" i="" mi="" |="" [nt="" i="" i="" ili="" a="" i="" variabl="" [1="" la="" |="" ll="" |="" i="" |="" wl="" teak!="" i="" i="" i="" |="" ni="" iy="" li="" |="" nl="" i="" i="" it="" i="" tr="" (a)="" are="" these="" two="" time="" series="" variables="" stationary?="" ti="" (b)="" what="" is="" the="" order="" of="" integration="" of="" each="" variable="" based="" on="" each="" piece="" of="" evidence.="" ~="" (c)="" estimation="" output="" is="" presented="" in="" figure="" 4="" below.="" interpret="" the="" marginal="" effect="" of="" variable="" "food",="" |="" in="" fi="" aire="" 4:="" estimation="" output="" call:="" im(formula="‘Case-Shiller" housing="" price="" index’="" ~="" food,="" data="x)" residuals:="" min="" 1q="" median="" 3q="" max="29.238" -9.943="" -2.793="" 12.787="" 28.424="" coefficients:="" |="" estimate="" std.="" error="" t="" value="" pri="">I1tl) | (Intercept) -150.08593001 6.35598100 -23.61 <0. 0000v00000000002="" i="" food="" 0.00174447="" 0.00003906="" 44.66=""><0. 0000000000000002="" wee="" i="" signif.="" codes:="" ©="" '***'="" 0.001="" '**'="" 0.01="" '*'="" @="" ps5="" ‘a1="" "3="" residual="" standard="" error:="" 13.98="" on="" 308="" degrees="" of="" freedom="" multiple="" r-squared:="" 0.8662,="" adjusted="" r-squared:="" 0.8658="" f-statistic:="" 1994="" on="" 1="" and="" 308="" df,="" |="" p-="" ii="">< hi="" i="" -="" nd="" hn="" i="" i="" ju="" 0="" |="" ju="" i="" l="" y="" .="" (d)="" what="" would="" you="" do="" to="" make="" the="" variables="" stationary?="" (e)="" the="" variables="" are="" now="" stationary.="" estimation="" output="" is="" presented="" in="" figure="" 5.="" did="" you="" expect="" those="" results?="" in="" comparison="" with="" question="" 2(c),="" which="" regression="" model="" is="" better?="" why?="" figure="" 5:="" estimation="" output="" call:="" ly="" im(formula="DCASE" ~="" dfood,="" data="diff)" residuals:="" min="" 1q="" median="" 3q="" max="" -12.8426="" -0.4490="" -0.1645="" 0.1658="" 26.1063="" coefficients:="" estimate="" std.="" error="" t="" value="" pr(="">Iiti) (Intercept) 0.09132 0.14312 0.638 0.524 DFOOD -5.20599 15.70901 -0.331 0.741 Residual standard erron: 2.458 on 303 degrees of freedom Multiple R-squared: ©.0003623, Adjusted R-squared: -0.002937 F-statistic: ©,1098 on 1 and 303 DF, p-value: 0.7406 5] Please cele file(s) Bela filets) I | hh wy rv ll li a (1