Estimation of Investment in Residential and Nonresidential Structures v2.0
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1 Esimaion of Invesmen in Residenial and Nonresidenial Srucures v2.0 Ocober 2015 In he REMI model, he invesmen expendiures depends on he gap beween he opimal capial socks and he acual capial socks. The general expressions of boh residenial and nonresidenial invesmen can be wrien as I = α(k K (1 I = invesmen in ime period ; K = opimal capial socks in ime period ; K = acual capial socks in ime period ; α = he speed of adjusmen. The speed of adjusmen measures he proporion of gap ha is eliminaed by invesmen each year and is he coefficien o be esimaed. In each ime period, he acual capial socks equal he capial socks a he end of he previous ime period depreciaed during he curren ime period, so he invesmen equaion can be expressed as I = α[k (1 d K 1 ] (2 d = depreciaion rae of ime period ; K 1 = capial socks of he previous ime period 1. The acual capial socks equal he depreciaed capial socks of he las ime period plus invesmen, such ha K = (1 d K 1 + I (3 1
2 Similarly, K 1 is calculaed as K 1 = (1 d 1 K 2 + I 1 (4 Using equaion (3 and (4, we replace he acual capial socks wih he depreciaed capial socks and invesmen of previous ime periods, so ha acual capial socks can be wrien as 1 K = K 0 (1 d i + I i (1 d j (5 K 0 = he inial capial socks. Subsiuing equaion (5 ino equaion (2 produces 1 I = α {K K 0 (1 d i + I i [ (1 d j ]} (6 The opimal regional capial socks for residenial and nonresidenial srucures are calculaed as shares of opimal naional capial socks. The opimal residenial capial sock depends on he regional share of real disposable income and he regional capial preference facor, such ha K R,r = β R r ( RYD,r R K RYD,u (7,u RYD = real disposable income; β = regional preference for residenial capial; R denoes residenial capial; r denoes regional; and u denoes capial. The opimal nonresidenial capial socks depend on he regional share of employmen, labor coss and capial coss, such ha ( ARW,r ( AE,r K N,r = β N ARW,u AE,u r [ ( ARC N ] K,u (8,r ARC,u 2
3 ARW = labor coss; AE = employmen; ARC = capial coss; N denoes nonresidenial capial. Subsiuing equaion (7 and (8 ino (6, we could ransform he invesmen equaion for residenial and nonresidenial invesmen ino I R,r = α R {β R ( RYD,r K R RYD,u K R 0 (1 d R i,u 1 + I R i [ (1 d R j ]} (9 ( ARW,r ( AE,r I N,r = α N {β N ARW,u AE,u [ ( ARC N ] K,u K N 0 (1 d N i,r ARC,u 1 + I N i [ (1 d N j ]} (10 α, β and K 0 are unknown parameers o be esimaed. To solve he equaions, we specify equaion (1 for he naion and he opimal naional capial socks can be expressed as K u = I u α + K u (11 Using equaion (9 and (11, we could solve for he invesmen in residenial srucures. For simpliciy, we le A R = (1 d i R 1 B R = I R i [ (1 d R j ] C R = β R ( RYD,r [ I u RYD,u α R + (1 d i R K 1,u R ] so he invesmen equaion for residenial srucures can be wrien as 3
4 I R,r = K R 0 ( α R A R α R B R + β R α R R C (12 Similarly, we use equaion (10 and (11 o solve for invesmen in nonresidenial srucures. Assuming A N = (1 d i N 1 B R = I R i [ (1 d R j ] ( ARW,r C N = β N ARW ( AE,r,u AE,u [ ( ARC,r ARC,u N ] ] [ I u α N + (1 d i N K 1,u we rewrie he invesmen equaion for nonresidenial invesmen as I N,r = K N 0 ( α N A N α N B N + β N α N N C (13 Therefore, he general final invesmen equaion for boh residenial and nonresidenial invesmen is I = K 0 ( α A αb + β αc (14 Daa We use panel daa of 50 saes and Washing D.C. from 1999 o 2013 o esimae he invesmen equaions for residenial and nonresidenial srucures separaely. The naional capial socks and real depreciaion rae for residenial and nonresidenial fixed asses are from he Bureau of Economic Analysis (BEA. The real disposable income in he residenial invesmen equaion is from he REMI PI+ V1.7. We use he privae nonfarm employmen, relaive composie labor coss, and he relaive capial coss daa from PI+ V1.7 for he employmen share, relaive labor coss, and relaive capial coss in he nonresidenial invesmen equaion. Real invesmen daa a he naional level are from he BEA privae fixed invesmen in residenial and nonresidenial srucures. The sae-level invesmen daa need o be consruced. For he invesmen in residenial srucures, we uilize he building permis daa from Census new privaely owned housing unis auhorized valuaion o esimae he regional share of he oal naional invesmen. Census provides daa 4
5 of privae nonresidenial consrucion pu in place by sae, which is used o esimae he regional nonresidenial invesmen expendiures. Esimaion and Resul To esimae he equaion, we loop over a range of values for α. In each loop, we rea α as known and plug he value of α ino he equaion. Therefore, he arge equaion is ransformed ino an equaion wih linear parameers. We apply fixed effecs models o esimae he arge equaion and record he leas sum of squared residuals for each loop. The value of α ha minimizes he sum of squared residuals is he final esimaed speed of adjusmen. The esimaed speed of adjusmen for residenial invesmen is Thus, 21.7 percen of gap beween opimal and acual socks of residenial capial are eliminaed each year. The esimaed speed of adjusmen for nonresidenial invesmen is 0.078, indicaing ha only 7.8 percen of gap beween opimal and acual socks of nonresidenial capial are eliminaed each year. The following able presens a comparison of esimaed speeds of adjusmen from differen versions of models. Our new esimaes are slighly higher for boh of he wo ses of regressions. Comparison of Esimaed Speeds of Adjusmen New Esimaes Curren Model Coefficiens 2001 Esimaes 1993 Esimaes Residenial Invesmen Non-residenial Invesmen
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