Three Essays on Canadian Housing Markets and Electricity Market

Three Essays on Canadian Housing Markets and Electricity Market by Yuan Zhang A Thesis presented to The University of Guelph In partial fulfilment of requirements for the degree of Doctor of Philosophy in Economics Guelph, Ontario, Canada Yuan Zhang, May, 2017

ABSTRACT THREE ESSAYS ON CANADIAN HOUSING MARKETS AND ELECTRICITY MARKET Yuan Zhang University of Guelph, 2017 Advisor: Professor Y. Sun, T. Stengos This thesis includes three empirical applications: spatial dynamic panel data model on Canadian housing market, impulse responses of Canadian housing market, and emission reductions of wind powered electricity in Ontario. Chapter 1 studies the spatial dependence of residential resale housing returns in 10 major Canadian Census Metropolitan areas (CMA) from 1992Q4 to 2012Q4 and makes the following methodological contributions. Firstly, in the context of a spatial dynamic panel data model we use grid search to derive the appropriate spatial weight matrix W among different possible specifications. We select the compound W with the minimum root mean squared error formed by geographical distances and the GDP levels. We further offer an interpretation of the selected W that is directly linked to the definition of the Arrow-Pratt risk aversion parameter. Secondly, contrary to common practice in the literature, we decompose our parameter estimates into direct and indirect effects and we proceed to derive and plot the impulse response functions of housing returns to external shocks. The empirical results suggest that Canadian residential housing markets exhibit statistically significant spatial dependence and spatial autocorrelation and both geographical distances and economic closeness are the dominant channels. Furthermore, in Chapter 2, we calculate impulse response functions and plot in 2-D and 3-D figures, and we find that special feature of the Canadian housing market is, as seen from the impulse response functions, that the responses to shocks do not spread widely across regions and that they fade fast over time. In Chapter 3, We use electricity output of 151 generators in seven fuel sources in year 2010, including nuclear, coal, natural gas, hydroelectric, oil/gas, wind, and wood waste/biomass, and aim to find out how wind energy affect the production of other power sources. We use three different models to estimate the marginal effects of wind powered generators on other fuel sources. The contribution of wind energy to the Ontario s mixed electricity supply system in terms of decreasing the electricity production mainly from coal, natural gas and hydroelectric generators, and reducing the air pollutant (CO2, SO2, and NOx) emissions. When wind generators produce one MW per hour, the marginal effects from other fuel sources is replaced less than one MW. Due to instability of the wind power, the backup power is needed. The backup generators are usually thermal generators that emit air pollutants, and the fuel uses are larger than they operate at a steadily power level, which is so called emission bias.

Therefore, this makes the net marginal effects and emission reduction less than expected.

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② r ②s s t r t r r r② r s t s s ② r t r t t r t r r s t t s t r t ② r t s t t r t t s t st s t t t ② r t r rt② r s t r ts r t s ② s st t t ② r r t s r ② t s s s r s t r s t ② r r ts r t ① s t r t t st s t s t s ① s r Pr ① P r t t r t ① s r t ① s s s s r ts t ts s r r s t r rs t r r t ① s s t r r r s r t r t r t ② t r t s P t r t r t s s r s t st rt t t r t t ts s ② t r t s t r r t r s r ② t ② s t ② st t r s s r s r ① t t ② t s P t ② t r t s r s r r t t st s r r r ② st t s r s t t ① t s s t② r s s ② st t r r r s s r s s s r s s t t s s s s s ② s r s ss t r t s r s t t st s ② r s tr s t q rt r ② tr s s q rt r ② t t ss t t t r t s t t t t t r s st t t ② r r s s t s t t tr ① r s s r r s s s ② t t s ss t s r t r st t ② r s t s r t t ② ② t q rt r ② t t t t q rt r ② s

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t rt r t s ② τn s t N 1 t r 1 s q t s s t t r r ss r r ss r t rr r t r t t r s t r ss s t ② t ① t s s s t t tr ① WN s s s t t r t s t rr t st r s ρ s t s t t rr t t εt s N 1 t r i.i.d rr r t r t ③ r st t r tr ① σ 2 IN r IN s N N t t② tr ① s st t ② q s ① t ① ts s t ② st t r t ① ts T s r r t t n t r s t st t r s nt s st t s② t t ② r ② str t r t t r t s s r t WN t s s s t t tr ① WN st t s t s t t r λ ρ r r② s s t t t s t ts t s r ② s r r t s t t tr ① s t st rt t ss s t st t r tr s t s r t r s r t r t ts t t r t r t t r r s r r s ② s t r s tt r t r r t st r W ② ② t s t ts r t r r st s st s t tr s t s s t t tr ① s s t s t s t r st r s tr t st t r t r t t tr s s t s s t rr rs ② t t r s ts t s t s t t s t s r t r s s t t rr t st r s s r t s

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s t st ② ss st ② t s t ② s t ② s s t rs st t t ① t st t t s rs st t s s r s s s t t wi,j s t i j t t t tr ① W t t② ② r ts t s t r i r j s t wi,i = 0 r i = 1,.., N t ① t s t W 0 t r t tr ① W q s W 0 ② t r st W 0 s t r ③ t r r s r s s t st t② r r s s Pr ② t t t st t i j ② di,j t t r st t tr ① W G,0 s r s s G,0 G,0 W G,0 = wi,j, and wi,j = d α i,j, i 6= j r α s t r r t r t t r t s rs r t G t s t r t r st s α s s ② s t q t r s t ② rs r t s s t t t s r s r t s r t r t t s t t tr ① r t α = 2 s s ② s s t r t② tt t s r t r t t q r t r s t st r t st s W s r t t s st t s st ② str t W tr ① s st t st s r st t tr ① r ② t ① t t t s

G,0 W G,0 = wi,j, G,0 = exp( αdi,j ), i 6= j and wi,j r t r α s s t t r s t t tr ① s s st s r s r t rs t t r ② s t str t t t r rs P r t t ② t s t t t r t② i t t② j s t ② t rs t t r r α = 1 t r st r ③ t s t rs t t t r t r t r α t r t t ①t r str t t t s t rs t t t t r t s r t② t r s rst t s r s s emp,0, W emp,0 = wi,j emp,0 and wi,j = empi empj α, i 6= j empi empj t s t r t t ② t s t t r s rs t s r s t r s t s r ② t t r t s t s t tr ① r ts t s ss t t ② t s t t r s s t W mig s r t t r t r t t t t s r migi,j s s s t rs t r t r r ts t r i j ② r r r t r migi,j = 1/number of migrants between CM A i and j r r r t r r ts t s r t migi,j t r ② t rs t s tr t str t t tr ① s t t ① t t r t s s s r t t t r s s s ② s t rs st t t t str t t t

mig,0 migi,j t s r migi,j s t r t t t s wi,j t r r s t r t r i j t r t s t r s r t t r r ③ t s r s s W mig,0 = wmig,0, mig,0 α = migi,j, i 6= j and wi,j t r t tr ① s r rs t i j s r s s mov,0 W mov,0 = wi,j, mov,0 = movi movj α, i 6= j and wi,j s t tr ① s s t t r rs rs r t t r t r ss ② rs r t s s ② r r ts t t r r tr r r ts ①t r r ts r r ts r ts r t r ss rt t tr ① s s P s s r s s GDP,0 W GDP,0 = wi,j, GDP,0 = GDPi GDPj α, i 6= j and wi,j s t tr ① s s t t r t s r t② r P s t t r s r r s t t tr ① s t s WN s t tr ① WN0 ② t r t r ③ t r r t s s t t ③ r s r mov i,j r t r ss ② rs r t s s ② r r r ss r t ② t t r r migi,j ② ts t r t i j s ② t s t t t r t r r ts ①t r r ts s t r s r r t t t ② r t rt t s s t t t s t r s t i j r r t tt r ① t s t s r t r s

0 w12 w13 w21 0 w23 WN = 0 w31 w32 wn 1 wn 2 wn 3... w1n... w2n... w3n... 0 rst r t r s t s t t t t rst tr t r t r tr t r s t r r s t r ts t r tr t r s t t s r t r t rst tr t r r ① t t w12 t s t s r t s r t r t rst r w21 r r s ts t t t rst r t s r t t t t s t t tr ① WN s t s② tr t st r ③ t t s t t t t r i s r j ② t t s s t t r j r i s t t t ts WN r s t s t r s t t str t s t t tr ① s t r t t W = aw G + (1 a)w E, a [0, 1] r W G s t r t tr ① str t ② t r t r t rs st t t r t t ① t t t W E s t t t t s s r W emp, W mig W mov W GDP s q t s t r t r a s t t t r s t s s t r t t s

s t rr s ② r s t s t s ② st t r t rs r t s t t tr ① ② r s r t t st r r t WN ② st t t t t tr ① r ② t r st s r t s WN = g (di,j, zi,j, θ) r θ = (αg, αe, a) αg s t r r t r r t αe s t r r t r t r st di,j s t ② t r r s s r t② zi,j s t ② s t r r t r αg r r t tr ① t r r t r αe r t s t tr ① t t r t r a s t s ② r t θ st t ② t t s t t θ t t ③ s t s t st t θ ② ② r s r r t s t t s t t tr ① W r t r r t t s s tr r② t r t t t r t r t s r ss s t t tr ① r s ts t s r t sts r ③ r r s rst t r t s r t r s r s ① t r ss s t

s P s r s t st s P s r r t r s r ss s t t t s t ts r s P s t sts s rt t t ② ① ts s t t t t s t t st t t s t t rr t rr r t r s s st t s s t r t ② t s t st r t t r ts r t ① ts s t s s t t s t s s t s t r s ts r st t r s ts t rs st t r str t ② s r ts r r s rs t r② st t r s ts q t s r st t ② q s ① t ① ts s t rst st t t P t r t s t s t s t t tr ① q t s t t rst sts t r s ts r tr t ② t t t s t t r t s s r t t t s s r r t t r s t st t s t s t rr r t r s t t r s t t st t r s ts r W s t r r st s s t s t r ss s t s ts r t s t rs t t t t r ts r t ② t t ① t t st s st r s r s ts W s t r t t ② t s t r r ts t t t r rs r P s q t s t s s t ② r r t s t s t

t st t s λ ρ r t s t t s t t rt s W emp s t s t t s r t② t t ② t s tt r ① s t t s t tr s t r t s t r ts r s t t r s ts t t t t rs t st t rr s t tr ① s ② WN = a W G + (1 a) W E r② a r t r② αg αe t t s t s ② st s r r a = 0.1, αg = 0.55, αe = 0.35. s t r s t st t r t tr ① s WN = 0.1W G + 0.9W GDP t t t t st t s r s r t r r r st s t r r t ② s t rs st t t r q t s t s t tr ① λ W r s t s t tr ①ρ W r s t s r ss t s r s r s t s②st s st t r② t s rt t t t t t tr s s s t s r t② ② ss t ① s r t ① t② ss t ② t r s P r s s ss st t t t s t tr ① r ② s t ② t t tr s s t t r s r t s r ② t s r s s s t tr s s t rs ② t t ② s t W r ② r st s t r P s s t t ① s s r t rs P s r t s t t s s t ss t② t t ② t s s r t ① t② r r r rr t t t t tr ① s t r r s r t ② ss t② r t r r s r

s r ss t t ② ① t r② r t t r ts s r t t t t ② t t r r s s r t t r s ss t r t ② ① t t ② r t rs t t r t ② s r r t s t s r ts s t s ② t t r r s t t t ① st t s t t r t s t t t ② s rr r s r t t r r s r r r r t r r s r q t s Yt = (IN λwn ) 1 γyt 1 + (IN λwn ) 1 Xt 1 β + (IN λwn ) 1 (µ + vt τn + ut ) ut = (IN ρwn ) 1 εt. t Sk (W ) t N N rt r t tr ① ① t Y t r s t t t kt ① t r② r X r 1 t r N t t t s ss r t t t t 1 t ② Qt 1 r q t Sk (W ) = E (Yt Qt 1 ) = (IN λwn ) 1 βk T Xt 1,k r IN s t N N t t② tr ① k s t kt ① t r② r ts i j t t s t ② [Sk (W )]i,j P t r t t r t t s r t kt r r s E(yi,t Qt 1 ) xj,t 1,k = [Sk (W )]i,j

r i 6= j E(yi,t Qt 1 ) xi,t 1,k = [Sk (W )] i,i r s t ② t ③ r t t kt ① t r② r r j t t s r t r s t r r s [Sk (W )]i,j 6= 0 s r t s r s t t s r t r s r i r ① t r② xi,k t r r s t ts Sk (W ) r r s t t t r t ts ts r r s t t r t ts r t t s r r t t s [Sk (W )] i,i r t ts tr ① Sk (W ) = (IN λw ) 1 βk r t ts t r i s t it r Sk (W ) ① t r t t [Sk (W )] i,i r t k t ① t r② r s r t t s rs s kt ① t r② r t r r s r i r t t r r i s s r ② t it Sk (W ) ① t t t [Sk (W )] i,i s r r t ts s r s s t kt ① t r② r r i t r r s t t r t t t s t r s r t ts r r ② q r t s t s r s r r s t r t t r r t t ts ② t s t t t r r t t r r t r st t s t λ t r s t s t s r t r s t r s s t r r s t s t s t r s t t r r t t t r t rs s r r r t s s t r t r λ s t t rr t r t r ρ r st t t 0.8038 0.9984 t ② r s t st t s λ s t s t r t t

r t ts r t s t s s r t t s t s t t rr t s t r r st t s r t② r P s st t t t r t s 2.6497 s st t st ② s t t t s t s s t r st r st t s s t t r rt t t t r t r s s r t t② ② t r st t s t t r t t t r s r t ts r t t ① t r② r s rst s t r t ts r r s t t r t r t r②t s r s t s r ① t t r t r t r r s s ② t r t t r s s r t r r s ② t r s q t r s t t r t r t t r r s t s r t r r r ② t r t r r s s ② t r r s s r t r s r ② r rr s t t s r r t t r s ss t t r s t r t r t s t r t t r t t t r r r s 1.28 st r t t r t t s t t r r r t r r s t t r r s ss t t s t r t r t s t r t s st t s r t s ② s r s s t t t r st rts Starts t Completed r st t st ② s t t t s r s t ② t r s r s t s t t r st rts t r t rs ① t r r t t r s s r t r s t r r t t t r r r s

r ② t r s r s t s t t r t t r②t s t r r t t r s ② t r r t t t r r r s ② ② t r t s ② s r s t t t r t s ② r t t ② st ② t s r s s t t ② s r r t s ② s r Starts Completed t s st t st ② s t r t s t t s r t r r t s Pr ① N HP I s s st t st ② s t t t s t s s r s s s rt r tr t r r ② t s t r s t ② t s r t s r t ① t t t s t ② rr t s s r s s s t t s st t t s s t r r t r s r s t ② r t t r r t t t st t s P s s r t t r t t s t② t r s r s s r t r r t r t t t r s s r t r r ts r s ② r st r t t r s s r t r r s s t r t s st r t t rs r t r r t t s t r s r s s r t r s r t r r s ② r Yt 1 s st t st ② s t t s t q t t r t r t r s ② r r s ② r②t s st t t r r t t r s s r t r t s ② r t r r t t r s ② t r s r t t st r t r r s ts t t t s r s r st ② t r r s t r t r s r t ①t r s r s ② ttr t t t r q ② s tr s t s s ② rs

st ② r t r s tr s t r t st t t t r t t s r s t st t st ② s t t t s s r s r s st r t s s st r t r rts t s r t r ① t r s r r t r s t r ② r t r s ② r s t t s r s s t s r ② rs s t ② t r t s r s t r s r s t s t t s r s t r t st r q r r t s t t s s s r r s t rt r s s t t s r t r s t s t r t s t r t t r rr Pr tt r s rs ① t W t s st r② t s ss ss t r t r s s ② r r t t s r r s r t ① t ss t s t s r t r s r s r r s t r t s t ts r r t t t t tr ① r st r ③ t r st s G D(di,j ) = d α i,j t st t s s αe G(gi,j ) = gi,j, and gi,j = GDPi GDPj

r i 6= j αg, αe > 0 ② r s r t st t t s t t tr ① q t r t r st ts ts r ts r t t s t s r t② P s t s ts r t r t ① t s t r t s t rr Pr tt s t r s rs A1 (di,j ) A2 (gi,j ) s s r s s t t② t r s r t r s r ts t s r ts t r A1 (di,j ) A2 (gi,j ) r s s t t t r t r s r ts t t rr Pr tt s r s t r s rs ss t t s A1 (di,j ) = 1 D (di,j ) = (1 + αg ) D (di,j ) di,j A2 (gi,j ) = D (gi,j ) 1 = (1 + αe ) D (gi,j ) gi,j r st di,j t st gi,j s t ② rr t t A1 A2 r s t ② t r r st di,j t s r A1 (di,j ) s t r r t ss r t② t s r A2 (gi,j ) t s t r r t r st ss r t② t s r s s t t② t r s r t r s rs ts t r r s t r s r r s s t t r t r s r ts r r ② r s r r s t t s r P s s r t r r t rs αg αe t r t r t r s s t t t r t r s r ts ② r s r rs s t ② s α s t t r r t α = 2 r r t r t② s r s αg αe t t t ② r s r rr t st t s α G = 0.55

α E = 0.35 t t ③ t s t st t s r t r t ② s [0.1, 4] t r t tt s s t t② t r t r s r ts s s t s st rs t t s r st s t s rt r ② ss s r P s r s s r ② r ② s r ts r s ② s r s r r t r ts t s s r r tr s tt t t t r r ② s ② r s rs sts s r s s r t s r ts t t r t r ② r t r t ② ② t s r r t r ts t ② r ss ② t t t t s t s s s r t t st rs ② s r s rs t s t ① t st ts s r st s ① r s ② D = exp( αdi,j ) r t ss t A(di,j ) = D1 (di,j ) D1 (di,j ) = α st t s s sts t t st s r t r t t t s s t t② r t r s r ts t s r ts s t t t s t s rt ② r r s ts s r t r s t t s rt r r t t s t t tr ① r rs r t r st r s t t t ① t st t t t r t t s t s t r st ② t s r t r s r s s tr t r s r t t s t s t s t t rr t ① st t s r ts st t ② s t ② t s r s r t r t r r t s t t

tr ① W r t ss s t s t r t s t W s t ③ s r t sq r rr r W r ② r st s t P s s s t t r r s t s t s r t r s r s t s r t s r t s r t② P s r s ss rt r r t r r t t t s t W t t s r t ② t t t t rr Pr tt r s rs r t r r t t r r t t t t r t r s r r t r st t s t r t r t ts t r s t s r s t r t r t t s r s s t s s r t r s t ①t r s s

t r t r s r s s s r t tr t s st ② s t s t r r s ts t r t s t ① sts t s t ts t t t rt r ① r r t t s t ts s r s s t s r s s r t r t r t t s s r s ② s s t s ② s t s r t r t r t r st ② t s t ② t s s t t t s r s s s t r t r ss t s st t t s s r t r s t t st t s r t r s s t r t s t t r s t s s ② t s tr s r t s r t rt r t r r t t t r st t r s ts st ② t s r s s t s t t r st s s t rr t t r r st s r t r s t s r s s t s t s ① q rt rs s s r s ss s r t ② t t s s t s t s ss s t rst s s t s s t s r t r s t t s ss s t s s s t s s t t r t s r s s t tr s t t t r t r r s s t s ② t s t q t r ② s t t t tt r rst t t s s s r t r s r t r ss

s s r Yt = γyt 1 + λwn Yt + Xt 1 β + µ + vt τn + (IN ρwn ) 1 εt s ② t t t t IN λwn = A IN ρwn = B rr Yt = A 1 γyt 1 + A 1 Xt 1 β + A 1 (µ + vt τn ) + A 1 B 1 εt st t s r s s t t s t r εt t η t t t s IRF0 = A 1 B 1 η Yt+1 = A 1 γyt + A 1 Xt β + A 1 (µ + vt+1 τn ) + A 1 B 1 εt+1 t + 1 s st t t q t t t Yt+1 =γ 2 A 2 Yt 1 + γa 2 Xt 1 β + A 1 Xt β + γa 2 + A 1 µ + γa 2 vt τn + A 1 vt+1 τn + γa 2 B 1 εt + A 1 B 1 εt+1 ss t s t t Xs vs εt s t ss t t t r r r s t X s εs vs r s t r r r ② s r t r s s s r t r t s s t s s ε t s str ss t t s s r t r s s s s t r s t s r t t t

t t r s ts Yt+1 = γ 2 A 2 Yt 1 + γa 2 + A 1 (Xt 1 β + µ + vt τn )+γa 2 B 1 εt +A 1 B 1 εt+1 rr s s r s s t r t+1 s IRF1 = γa 2 B 1 η t t s r r Yt+2 =γ 3 A 3 Yt 1 + γ 2 A 3 + γa 2 + A 1 (Xt 1 β + µ + vt τn ) + γ 2 A 3 B 1 εt + γa 2 B 1 εt+1 + A 1 B 1 εt+2 Yt+3 =γ 4 A 4 Yt 1 + γ 3 A 4 + γ 2 A 3 + γa 2 + A 1 (Xt 1 β + µ + vt τn ) γ 3 A 4 B 1 εt + γ 2 A 3 B 1 εt+1 + γa 2 B 1 εt+2 + A 1 B 1 εt+3

Yt+h =γ h+1 A (h+1) Yt 1 + γ h A (h+1) + γ h 1 A h + + γa 2 + A 1 (Xt 1 β + µ) + γ h A (h+1) B 1 εt + γ h 1 A h B 1 εt+1 + + γa 2 B 1 εt+h 1 + A 1 B 1 εt+h rr s s r s s t s r IRF2 = γ 2 A 3 B 1 η IRF3 = γ 3 A 4 B 1 η IRFh = γ h A (h+1) B 1 η r h = 0, 1, 2,...T. r r t str t t t r r s r s s t t t st r rr rs r t IRFh t t s s t t t st r rr r t t r t t tr s r t t r s t t t r t r t ② t ② t s② t t r t tr s r r t r s V ar(irfh ) = IRFh IRFh IRFh,, γ λ ρ Σ 1 IRFh IRFh IRFh,, γ λ ρ

r Σ s t s② t t r r tr ① t st t rs γ λ ρ t str t t t r ˆ h) ˆ h ± 1.96 se(irf CI = IRF ˆ h s t st t IRFh t r t s IRFh r t IRF r r t str t t t r t t t st r rr rs r t st t s IRFh t ② t t t r t s IRFh t r s t t r t r (γ, λ, ρ) r r h = 0 t h = 6 r r s t r t h = 0 s s t t ② η t IRF0 (γ, λ, ρ) = (IN λwn ) 1 (IN ρwn ) 1 η =A 1 B 1 η r t IRF0 t r s t t (γ, λ, ρ) s

IRF0 =0; γ i d [vec (A 1 )] IRF0 h 1 T = B η IN λ dλ i h h i d {vec [(A 1 )]} d vec IN λ WN T = B 1 η IN dvec (A) dλ ih i h T T = B 1 η IN A 1 A 1 [ vec (WN )] i h T = A 1 B 1 η A 1 vec (WN ) ; d [vec (B 1 )] IRF0 = ht A 1 ρ dρ d [vec (B 1 )] d [vec (IN ρ WN )] = η T A 1 dvec (B) dρ i h T = η T A 1 B 1 B 1 vec (WN ) h i T = B 1 η A 1 B 1 vec (WN ) r r rs t t r r r t WN tr s r s r t + h WN vec (WN ) s t t r ③ t tr ① t t r r h 1 IRFh (γ, λ, ρ) =γ (IN λwn ) (h+1) (IN ρw ) 1 η =γa (h+1) B 1 η r h 1 t r t IRFh t r s t t (γ, λ, ρ) s

IRFh =hγ h 1 A (h+1) B 1 η; γ h+1 X (h+2 j) 1 IRFh h A =γ B η A j vec (WN ) ; λ j=1 h i T IRF1 =γ h B 1 η A (h+1) B 1 vec (WN ). ρ s r s s t s s t t r s r t r s st t t s r s s t ts t s s t s s r t r s r t r st t r s s s r r② r t s ② r t t s r s s t ts s t s t r r t r② s r t r s t s t s r s r t t r s r t t t s r s s t s t r s s s t t s r t ts s r r ss t r ③ st r ③ s t s ② t st r ③ s r r r ② t s ss t r s ss r t s r r t ② t r ③ s t r ② t r t r t t r t t r r t t t t r s t s t tt r s t r s s t s t r s r t r s t r s s r s r t r s ② t t q rt r s t s s t st t ② r s s t r s r t r s st t ② t s t st t t t r s s r t r s t q rt r s s r② s

r t r s r s t st t t rs s s t ② s t t t r s t r q rt r t r s s t s t r② s r t r s ② st t ② t r s s r t r s r s st t ② t ② s t ts t r q rt r s r t r s t r s t st r s s t t s s st r t s r t s r t r t s r t r s r s ② st t ② ② t rst q rt r t r s s r t r s r s st t ② ① t r r② t tr s r t r s r s t st t rs s s s t ② s t t t r q rt r r t s s ② st t s t t s r t r t ② q ② t r t r s ts s r r t t st t t t s t s ① t s s s r r ss st s t t s t t t s r r t t s r s t t r t r t ② s t t r ③ st r ③ t r r s s r t r t s ②s st r r t r r ss s t r s t t s s r r ② t s ss r t s r ts t r t s s s t t t t s s t r r t r r s ② t t s r t t r s ss r t s r s r t t t r ③ t ① s tt r ③ t ① s s t t r ③ r q rt r ③ r t q rt r s ① t r s s t ② s r ss t s st r t t ② s r ss t st s s s t s r r s s r s t s r st tr② ② t t r t r t t t s r s t t rt② s t s r t ② t r r t rs r t r ② r

t r r st r s t s s r t t t s t s t r st t t s r t② t r s r P s t t s t r t r s st t t st t st ② s t t s r s s t s s t ss r ss r s t s t ② t r q rt r ③ r s t t st t t s t s s r s t t s t t r s s t s t t t r r s s r t r t st r s r r t s t t r r s r r t r t r s s t r r r t s r② t r t r s r t tt tr ① r t t s r s s t s t s t t t r r r t r t r s r t r s r ① s t s t s t r r s t s r t r s ② st r t t r r ② r s t ② t s s ② st t s t r t t t s r s t r s t r s st r t s t r t t r r s r t r r s ② r s t ② t r s s r t r s r s st t ② ① s r t r s t t st ② t r ② t r s st r t s t r t r② t t s r s s r t r s r s t r s s r t r s r s st t ② tt s t st ② t s s t r s t t s s t st q rt r s t s r t r r t r s st r t s t t r r r t tt tr

① t s r s s r t r s r s st t ② t r s s r t r s r s st t ② t r s t st r s s t t s s ts s r t r s r s ② t t t t s r s s s t s t t t s r s t t t s r s s s t s s t t s s r r t t s s t r s s s s s s t t s s t s t ② s t ② r t ts t t r r t s r s s s r r t t r s t s t s t t s t s s ② st t t t s s s t rs st q rt r t s r t t rs t r q rt r t s s ② st t ts r s t t r s t r ③ ③ r r ss s t ts t r t s r s r ss t t s r r r s r ② t st r t s r s r t t t ① s tt ① s s t t r ③ r q rt r ③ r t q rt r s ① s r s s t s t s t t r t s t st t r s ts t st t t t r t r t s s t r st r t st t s t

s s t t t r t s t ② t r t t ts r s t s r t r s s r s t r st t s r s s t s t t t r t s s st r t s t t t r t r t t r t ② s t tt r s t s r s s t s rst t t t s r s s t s t s t t ① t r② r s Xt 1 r Yt =γa 1 Yt 1 + A 1 Xt 1 β + A 1 (µ + vt τn ) + A 1 ut Yt+1 =γ 2 A 2 Yt 1 + γa 2 Xt 1 β + A 1 Xt β + γa 2 + A 1 µ+ + γa 2 vt τn + A 1 vt+1 τn + γa 2 ut + A 1 ut+1 Yt+2 =γ 3 A 3 Yt 1 + γ 2 A 3 Xt 1 β + γa 2 Xt β + A 1 Xt+1 β + γ 2 A 3 + γa 2 + A 1 µ + γ 2 A 3 vt τn + γa 2 vt+1 τn + A 1 vt+2 τn + γ 2 A 3 ut + γa 2 ut+1 + A 1 ut+2 Yt+h =γ h+1 A (h+1) Yt 1 + γ h A (h+1) Xt 1 β + γ h 1 A h Xt β + + γa 2 Xt+h 2 β + A 1 Xt+h 1 β + γ h A (h+1) + γ h 1 A h +... + γa 2 + A 1 µ + γ h A (h+1) vt τn + γ h 1 A h vt+1 τn + + γa 2 vt+h 1 τn + A 1 vt+h τn + γ h A (h+1) ut + γ h 1 A h ut+1 + + γa 2 ut+h 1 + A 1 ut+h r IN λwn = A t N 1 t r ψ t t s t r t t t t 1 βp s t t r t t t r t t rr s s r s s t s r t st r t t r t s st st

IRF0 =A 1 ψβp IRF1 =γa 2 ψβp IRF2 =γ 2 A 3 ψβp IRFh =γ h A (h+1) ψβp q t s t r s s q rt r t t s s r rr t s s r s s t r ③ ③ r s ② t t t q t t str t t t r r s t r t s t t r q r t str t t rr r s r t t r t s t t r q r ② q t t str t t t r t s r s s t s t t r t s t r s t t r t rs s γ λ βp r A = IN λwn βp s t r t r r t t t r t ψ s N 1 t r t s t s t t t r t t r ③ ③ r h = 0 IRF0 = A 1 ψβp t r t IRF0 t r s t t (γ, λ, βp ) s

IRF0 =0; γ i d [vec (A 1 )] IRF0 h = (ψβp )T IN λ dλ i d {vec [(A 1 )]} d [vec (I λw )] h N N = (ψβp )T IN dvec (A) dλ ih i h T = (ψβp )T IN A 1 A 1 [ vec (WN )] i h T 1 1 vec (WN ) ; = A ψβp A IRF0 =A 1 ψ. βp r t + h r h 1 IRFh = γ h A (h+1) ψb r h 1 t r t IRFh t r s t t (γ, λ, βp ) s IRFh =hγ h 1 A (h+1) ψβp ; γ h+1 X (h+2 j) IRFh A =γ h ψβp A j vec (WN ) ; λ j=1 IRF1 =γ h A (h+1) ψ. βp r s ②s t s s r t r s t st r t s t t t r t r r② r t ② r s s t t s t t r t s r r r ts r s s ② st t ② t s s s t st rt r q rt r s r t r s r s

st t ② t r st s t r ③ ③ r r② r s s t st ② t r s st r t s t r② t r t r② q rt r ② s r t r s r s ② t r s s r t r s r s st t ② t r s s s t st t r s t s s t s r t t r t t s r t r s r t ts r s ② st t ② t ② s t q rt r r st s s r t r r s st t ② t r ③ ③ r ① s t t st t r s q rt r ② s r t r s r t t s t t r t s t s r t s r t ② r t t t t s s s r r ② t r st r t s r t r ③ t ① s r r s r t t t r s ss r t s r tt ① s s t ② r ③ r q rt r t q rt r s ① s r t t t ② t s r s s s r ss s s st r t t t ② r s t r t s t t r s t r s s t s t r t r t t r r t r t r s ② r s t ② s r t r s r r s st t ② r t r q rt r ② s r t r s r s ② r q rt r ② s r t r s r s ② t r s s r t r s r s st t ② r s s t t s s s t t st t r s r s s t t s t s t r t r② t t s r s s r t r s r s st t ② t t r s s r t r r s st t ② s s t ② s t t t t rs st t t rst q rt r tt q rt r ② s r t r s r s t st ② st r r s ②s t s r s s s

t t s t s t t t r r t r r t tt tr ① r t r s r t r s r s st t ② t s t q rt r t ② s st t ② t t t r st s t r ③ ③ r t s ② t q rt r ② s r t r s r t t st ② t s s t r s ② t r t r s t r t s r r r t s r t s r t r s s r r ss r s t r ③ ③ r t ts t r r s t t s r s s s t s r s r tt r r ③ s ② s t ts s s t r s t s r t r s r r t r t r s r rs t r tr s s s s r t st r r ss t s r ts t t r r s s t ② ② P s r t r ②s s t s t t r s s r s t t ② t t s t s t s r s s r t t r r s r ② r s r s r ss t tr② t t s t s r t r q st s t t r r t r s s s t t s r ② st t s s r s r t s r ss s r t s t s s r s r ss s t st t t ② rs s r s s s s r t r s r s t s r ts s r ts s s t r ② ttr t t t s②st rt r t s s②st s ② s r s t s st s②st t r t s rt r t r r t r t st r t r s s rt r t s t t s r ① t ① rt ③ t r r t

s r rt s s r r t ② rs t ① t r r rt s s r r t t ② t r r rt s s r s r t r str t t② r t r r tr s s s s r t s r t t ss r t s s s s s ② s t t t ②③ t s t r s t r s s r t r r ss r s r t t s t r st t t s s r t r s t t st t s r t r s s t r t s t t t s s s ② st r s rt t r ③ t s r ② r ss s s s s t r r t s r t r t r tr s t s r r r t r r s r t r ① t r str t t t s t ss s t t tr ① W t t ts ts t t s s t r st r r t r s t r s t r r t t r r t r s r r ①t t rr t P r tr t s r tr tt t t t r t s t t t g(w ) r r r s t t t s t t t t t st t ss s t t r rt ① r t t t② t t tr ①

t r s r r ss s t r tr t t r s t r ss t r r ② t r r t r r s t r ② ② r r t t ss s r r ② r r ② ② t t t r s ts tr t② s ② ① t r r s st s ② t r r r s s s r ② r r ② r s t r tr t t t r s t t tr t② s ② r t r r t rs r s t t s r ② s t r t ② s st r r ② t r s tr t② r t r r s ① r r r t s r t t t tr t② ②s t r t r r r tr t② t t t r t r s t t tr t② t t ② t r s tr t② s r r tr t② r t r r s ① r r ② r t t r s ts ② t r s r ② r t s r ② s t r t ② s st r r ② r t t t r str② r ② t r st t t② r r t st t t t ② s ① tt s P s P r r ② ss t r st t②

t r s t t r t r s t t r ② r t s t s t r s r t tr t② t tr t② t t r t r r r ② s t str t s st ② r t ② t s t r s ② r t tr t② t s str t r s s t r s r r t t tr t② r ts t s r s t r t s t r s t t s t② ② str r t ts t ② t s s str r t r t s r s r s ts t t t t r s t ②s r st r tr t② t t ② s ② t s t r t st t st ② s r tr t② s s r s rt ② r r ② r tr st t s s t s t② s r t rs r tr t② t st t r r t s r r t rs r ss t r② t r t ts t s st t t r r r t s r r t rs t r r t rs r t r s s r ② r tr st t s r r t q ② st r r t rs r t t t r t t r s s st ss r r t rs r r r r s s s r t ts s r r t rs r s r ① 2 s r ① 2 tr ① s X t r s st r t rs r s 2 X t t r r ts t t tr t② s ② s②st t② ② r s r ts t t st r r t st r s ② t ss r ts t t r s st ② rt② tr t② r ② t s t ② q t r s tr t② r t t r ② tr t② s t s s t st r t r t st rt r t t r s s t r t t r s s t ① t s s

t r r t t tr t② s ② s②st s t t t s ② t t t t r tr t② t t s t t ② t ① st t s st t t t r t s t r ② t r r ② t s r s t ① r t t r t ts tr r ② t t r s tr t② s ② r ② ②③ r ② tr t② t t t r t r s r t rs ② r t r t r r ② s r ts s r t r t r ② r s r s t r t ts r s s t r s r s r t s r t t ss s r s t st r s r r ② t st st t② r tr t② r t t r t t r t r s rts r r ② r ① s t ① st t r t r r ② s rts s t s ts s s 2 ss r t s r t s r t tr t② r r t s r ss ② r t t s s t t t t r r r t rt ss r ② s s s s r ② st t t r t st ② t ts r ② r t r s r s s r t s r t t r t s ② t rs á ③ r t t r t r r r t r s t t tr t r ② t s r s t tr t② r s②st s r s t ② t t r rs t t t ss r ② t r t r s s s r r t t

ss s r t r t s t rst t t ② t r t s st t t s r r s tr t ② r r t q t ② r t ts s r q ② t r t t t r ① s tr t② r t r t s ② s r t t s t rt r q ② tr t② t t t r r t r t s ③ r s t r t r② t s t r r s s tt ts t s t s ③ r t r r ② r t ② r s t r r r tr t② r t r r ss r t r r r s s r r t t tr t② t t t r ③ r s r t tr t② r t rs t r r r s t s t t s t s ③ r t r r t r t t tr t② t t r t r s t② r ② r r s s t ① s r r ss rs r s t r t t ts t② s t r ② t ③ r t r r r st t t t s r s t rst tt t t r r ② t ③ r t r r ss t t r q ② r tr t② t t t s r t tr t q s t s t r ② tr t② t t r r t rs s t r ② tr t② t t r t r s r ② s r r r s t s t t ③ r t r r r t t r ② s r r r ss r t ① st t r t r r r s t s r ① t t ttr t t r s r rs r t r st st ② t ts r ② ss r t s r r q ② r tr t② t t t t r s tr t② r t s s t t str t t

s ss r t ② r r r s ts s t t t t r r t r s ② ② rt t r s t t ss r t s t t t r r t s s rt s t r t r t ss s r ② s r r r ss r ① r t s t r t t r ② r t t r r ss r s ① t r tr t r② t t r s r s r t t t t r r t rs t s t ② st t r tr t② t t s t s r t t t r t tr t② r s r tr t② ② r t t r r r ss r r t t r t tr t② r s t r s r tr t② ② r t t r r r ss r r t r t t t r r r ss r st t s t s st t t ts r t r st t s t s st t t ts t r s t s t r t s t t s r ② tr t② t t t tr t② r t rs t t r ② tr t② t r ② r r tr r t t t r t r s r t st t s r t s r t rs t rs t t r r s t r ② tr t② t t t s t s r

r r r t rs r r t rs r t rs t r s r t rs ② r r t rs s r t rs st ss r t rs t r ② r r r t rs r t r r t tr t② r t r r ② r r ② r t t t tr t② s ② t r r s t ② s s t st t t r t r s s st ss r r t rs r r r r t t② s r t ts r s r t rs r s r ① 2 s r ① 2 tr ① s X t r s st r t rs r s 2 ① t tr t② r t r t r s s st ss r ② t r t t tr t② s ② t r r s t ② r r r t s s t t r r ② s t r t s r t r r ② r r r t r ② r t t r s t r t t r r s t t t t s t r tr t② s ② r t② s tr t② s rt t r s t tr s ss r s r t t t tr s ss r s t r s t r t t t r rt tr t② ① rt tr t② tr t② s ① rt t r r s st t s t s t t r t r s t t tr t② s s t t ① rt tr t② 2 th r r ss t r s r ② t r st r ts t r s ② s s t r t t r r ② r r r t r t r t r ②s r r t t

tr t② t r r r ② t r t r t r r t t t s t tr t② r t rs r s ② t s t t r r s r s ② r r t rs r s ② t s r rs r s r s r t r s str r t st t s r s ② t s r r s r s s t t s t② t rs t s r t r② r t r s t r t r s t t t r t s t s r ts r st t st t r t t r t r t r t t r st t tr t② r t rs t st t s s t t rs s t s r s t t t r r t r s t r t r t r tt r r ① t t tr t r t r t t s t s s r s t r t r t r r t rs s t t r t r r s s s s t s t s t t② t r t s r t s t s r② st t st s t r ② r t tr t② t ts r t② r ② t r t r r ② tr t② s t t tr t② t t r t r t s r ② s r s s r r t s ①t t st r rts t r t tr t② t t r r t② s r t t r t rs ② t r t r s t t tr t② t t t t t s r r r t rs t st t t② r t st st t② r ② r t r t rs t s st t t② st t② r t t r r ② tr t② t ts r t r r ② r t r s r t rs r s tr t② ② t s t t r t r r s s s s r t t② t r s t t r t r t t r t t r s t r t t r s t t q t r t r t rs t r s t ① t r r ss t t t t r t r t s r r ss r

r s r t t r t s r r s r s r tr t② s t st ② s t t ①t ② r ②s t r ② s ②s s t t t s t r str ② r s t t r t t r ② s t s t t r t s rt ① s r s s r s t t t r r r ② ① ts r t st ② t t t t t ts r ② r t r s r ② ① t s r ② tt r s t t t r ② s r r t rs r t st t t t t tr t② s r r s str r s t st t t t t s t ts r t s t tr t r t t r s tr t② r t t t t r t r t② s r ss s s r t s r t t s q st r s t ②③ r t t r r t t s rst t s t t tr t② t t t r r② r t r s t t r tt t t ① r t r t t r t r tr t② t ts t t ts r t r r r t t r r ② s r s r t t r r t r ② tr t② t ts ② r ② s r s t t r ② t ts r r ② s r s r t st t t tt t r r ② r s rs tr t② tr t② Pr s

t t r s t t st t r t ② t r t r tr t② t ts t t t ts r t r r ② s r r t ② t rst s r r r r ss r ② s t t r t r t s s t s r r ② tr t② t ts r r t rs s t t ③ r s r t t r r t ③ r t t s r t r s ② r tr s st r t rs r s t ② t r s r t t s r s r t tr t② t ts r t r t s r ② s r ② s s ① s r ① t t r s t s t s s t t r ts r ② t r t ②s rst st t t r ts r r t r s r t t r t t r ts ② r ② s r r t tr t② t ts ② r ② s r t st t t r ts r ② t r t r t rs r ② t s t② r r r r ss s r r r ss t 2 + αi Xt + γi Zt + ηi Oi,t + εi,t Yi,t = β1,i W indt + β2,i W ind2t + ρi dt + δ1,i Ti,t + δ2,i Ti,t

r i = 1, 2,..., 133 t = 1, 2,..., 8760 εi,t s t rr r t r t ③ r t r t r Yi,t s r ② t t r t it r t r t t t r W indt s t r ② tr t② t t r r t rs W ind2t s t sq r t r W indt r dt s t r ② tr t② r t t r r s Ti,t Ti,t2 r t r ② t r t r t sq r t r t t r t r r s t ② r t t r t r s t s r Xi,t s tr r s t t r r r t rs rs t t s t ② r W indt 1 W indt 2 W indt 24 W ind2t 1 W ind2t 2 W ind2t 24 dt 1 dt 1 dt 24 Ti,t 1 Ti,t 2 Ti,t 24 r s Xi,t r s t tr r ② str s r s ① t t s s ss t t t r s s s t rs r r t ts r t r Zt s ② r s r ②s rs r Oi,t s r t ② r t ③ r t th r t r s t r t t rs r r t r t s t t t t r t rs r t s r t r t r ss r t rs r q t t t r ts r t th r t r s r t t t t s s E (Yi,t W indt, Γi,t ) = β1,i + 2β2,i W indt W indt 2 = dt, Ti,t, Ti,t, Xt, Zt s r t s r r ss rs q t M Ei,t = r Γi,t ① t W indt W ind2t r t t r ts r r t rs r r t s r ② s r s t t t t tr t② t t s r t② t t t t r s t t t r ② r t t t

r t q t ② r t s st t t s r ② s st t ② t r st sq r s r t st t t r ts ② r t r t rs β1,i β2,i ② t r st t s r s r ② s t t r t r t ts t s t② str t r r r s r t s t s t r t r ② tr t② t t t t s ② ③ r s t r t r s t s r t s t s r r r rt r t r t r q t ③ r r s s tt r ② t s t s t t r r t s r r t s t s r ② st t t s r ① t t t t s t t t t t t r s t ② ③ r r ③ t s t r t s s s 2 + αi Xt + γi Zt + εi,t Yi,t =β1,i W indt + β2,i W ind2t + ρi dt + δ1,i Ti,t + δ2,i Ti,t Yi,t = max Yi,t, 0 r i = 1, 2,..., 133 s t = 1, 2,..., 8760 r t r s r t s t s t t r t ② r s t ts t s r ③ r t r ss ② q t

r t t r t r s ① t t t t t t s ② E (Yi,t β1,i W indt + β2,i W ind2t + λti Γi,t W indt, Γi,t ) =Φ β1,i W indt + β2,i W ind2t + λti Γi,t σi β1,i W indt + β2,i W ind2t + λti Γi,t σi +ϕ σi r λi = [ρi, δ1,i, δ2,i, αi, γi ]T Φ ( ) ψ ( ) r t t str t t r t② s t② t st r r r r t r t r t it r t r s t t t t t s ② E (Yi,t W indt, Γi,t ) W indt β1,i W indt + β2,i W ind2t + λ i Γi,t =Φ (β1,i + 2β2,i W indt ) σi M Ei,t = r q t t q t s t t t r t r r t t s r t r t t t r t r r r ss s t s t t str t s ②s ss t r q t rst t r ts r t t r rs r s t r t r ③ r t t r tr t② t t s r s t s ① st t t r t r t r s t t rst r r t t r ts ② t② rst r t t t ts ② t② r r r ss t r t r ② t ts r

t s ① r ② s r s t t t r ② r t ts ② t s s ① s r t r r t t t t s ①t s t t ① s r r ss rs s s tt r s ② t rt t s t s p, d, q Ö P, D, Q S r t s s r t S t s rt t r t t s s t② p P r t r r r t r r ss rt t d D t r t s t t t t s r q Q r t r r r r rt t r s S = 24 r ② t s t s t r s s r r s s di S i Φi B S φi (B) D θi (B) ui,t + β1,i W indt + β2,i W ind2t S Yi,t =Θ B 2 + ρi dt + δ1,i Ti,t + δ2,i Ti,t + α i X t + γ i Zt 2 r i = 1, 2, 3, 4, 5, 6 t = 1, 2,..., 8760 r ui,t s t s 0, σi,u r dt Xit Zt W indt W ind2t r t s s t T i,t q s t r t r t r ② r t rs r ② s r t r Yi,t s r ② t t r t r t th t② t t B s t r t r d D S st r s s s s r r t r t t t di Di r t r r t i t Φi ( ) φi ( ), Θi ( ) θi ( ) r ② t s r r P p Q q r s t ② r q t t t r ts r s s M Ei,t = E (Yi,t W indt, Γi,t ) = β1,i + 2β2,i W indt W indt

r i = 1, 2, 3, 4, 5, 6 r Γi,t t s st r r s Yi t rr t st s dt, Xi,t, Zt, W ind2t, T i,t r r ② t t t s t s r s t t r r t st t r t t s r s s s s t r ts s r s s t r t t sts t t st r s ② ② r r r s ② r t t st s t r t st s s t r ts t t r r q s ② t r ② t ①t t t st t ② t r q ② s s r t s t t ② ② r tr t ① ts s s t r t r q r s rst r t tr t② t t t r t r r ② s r s r s s ② st t r② st t t s ② ③ t t s sq r s tr ② r r p d q P D Q r t r ② ③ t ② s r t r t r r s tr s s s s r rs ② t ① s s t r t r t rs q t ② t r st t s s r st t r ts r t r t r r t r t② s t r r s t r r r r t s s t r t t sts r t s s ① s t ② t s t r r t s rst st s t r st t r② s s t② rst r ② r tr t t t t st t r② st t r② s q s r s r t s t r t s p d q P D Q t r t s t s s t t t rr s p d q P D Q

r r s ts r rts r st t r ts r tr t② r t ② t② s t r s r r t r t r t r s ② r st ss r t rs t r t r s r r r t rs t r t t s s r r s ts t s t ② r r ts s t s r s ① t t t r s t t t t r r s t t r t s t s ts rst s ① t tr t s t r r t rs r tr t② s t s ② s r t ① t t r② r ② t ts r t t t t s s s rt ② s t s ts r t t r s t st t s r r t r s r r s t t r s t t s ① t t t t t t s t r t t② s s r r t t s ts ② s s s r r s t ② t t r s s r t t t s t s t st r ① t t t t r t s s s t ② ttr t t t ss r ② rt r t t r rt s tr t② q s st t r s tr t② t t r r r t rs r r ts r s r r r r s s r t t t r s s st t t r t r s r t r r ② s s s ① t tr t s t s ② r r t rs s r r ② t t t t ① t s s ts ② r r t s

s r s ② r st t t t s ts r r r t rs r st t t t s ts r t r s r r t rs r t r r r s ts s rt t t s ts ss s r r s r ② q t ② ss r t s r ① 2 s r ① tr ① s X r s t r st t s r ② r tr r t rs r t s t r t② s r t rs t t ② r t ts s s r ① 2 s r ① 2 tr ① s X s ③ r s r r rt ss s ts r t t r r t rs r s t s t r tr t② t t s ts t s t r r ss r t s ② t r t rs t ss s r t r s s st r t rs t r ss r t s r t r s s r r t rs r s 2 r r t rs t ss r t s r s s r s t ② r t rs r s X t r s s st r t rs t ① ss r t s r s s s s r s t ② r s t t ss s ts r② s r ② r s t r t t r s s t ② s r r ss s ts t t r r r r ss r ① s ts r st t t s r r s t t s r t r t t r st t r s s s ② s t t t s ts t r s r s r t s s ts ① r s t ② s t t s s r s t ② t s ss s ts r r t t s s r r r t s

s r ss s ts r r s r t s t ss r t s r t r r ss r t s t ss s t rs ② r r r s r t t t ss r t s t t ss s t r t r t r t s tr t② r t rs r t st t ② r t st ② r ① t② r t rs r t t rt t② ② r s ss r t s s r s r r r r q r s t r r t r r t s r s s s t r s r r t t ② s ss r s r ① t③ st t st ② r ss r t s ② s r r ② ss s r t s r s t r s s②st r ② t t s r s t ② ss ② ② rs r t st s②st t ② ① t r t s t tr t s r ② ① t r t s t rst s②st r s s ss s ② t s t ① t r t s t r r t t t r t② Pr ss rs ss s r s ② s s ts st rt s t t s s s r s s t r t t t ① s t ② r ss s t t t s r t t ② r t ② s s s t r t s r r r t r t r ② r tr t② r r t r st r tr t② t r s rs r r q r s rs t t t r s

tr ss r t r t s r ② t r r t r s t st t r t ts tr t② r t r r t r ② s r s ② r t r t r ts t r t ②s r t r r r r ss s t s ② r t t r rst ② t r t r r r② r t r t r t t r ts ② r ② s r r t s ② r t t r rst ② r t tr t② t t ② r ② s r t t t rr s r ts s t t s r s t s t ② r t t t ss s t ts t t r r ts t rt r r tr t st ② r t ss r t s r r q ② tr t② t t t

r② t t st s r s t ① s r t r s Yt st rts Starts ts t Completed s t P r ts BP s str t ① U W I s r ① N HP I t ① Rent P t r t pop ② t t unem s inc r st s km r t t ② t emp rs s tr r ts ② rs r P $1, 000 s rs 1, 000 rs s t r ① t r② r s s s t rs r s s s t t tr ① r s ② P r r t s s r ② r t r st s r t r s t t s r s r t ① s t s ① t tr r t t r tt t r t s t r② rt t rt r r t s t r r t s

r ss s t s t t ② ts H1 H0 H1 2 > 0 σµ ρ 6= 0 2 > 0 σµ s r rr t rr r t r s ss H1 εt s r rr t rr r t r s H0 ρ 6= 0 ① ts H1 ss r ts s t t rr t s ts H0 H1 2 =0 H 0 ρ = σµ r ss s t H0 s t r t ② t s s 1.5037 24.3421 37.7409 52.5103 8.1093 st st t st s 0.22401 5.178e 06 1.998e 09 3.958e 12 5.092e 16 p R s t r s t st s s t r rr t ② r ① st t s s ① ts t t s r rr t εi,t ② t s s t t st tr t s t t s t t tr ① str t s rt r ss s t t ② s t P r ②r r t s t r t t st r s t s s t tr t ② s t s t st t s P s r s t st r rs t t t st P s r r s P s t st s s r s P r t s t st t t st r s t s t s t st r s t s s s t t st r s P s t st t ②s ① t P s r s t st r r ss s t s sts sts s t

0.0060 0.0083 0.0019 0.0031 0.0003 Completed BP 0.0383 0.66836 σ 0.02032 0.0382 (0.0375) 0.0055 (0.0097) (0.5668) 2.1758 (0.0029) 0.0045 0.1425 (0.0238) (0.1280) 0.1241 0.0022 (0.0038) (0.0034) 0.0078 0.0062 (0.0033) (0.0339) 0.1139 (0.1728) = empi empj 0.01963 0.0216 (0.0371) 0.0060 (0.0093) (0.5780) 2.7144 (0.0029) 0.0043 0.1350 (0.0249) (0.1311) 0.6466 (0.0037) 0.0017 (0.0033) 0.0079 0.0054 (0.0031) (0.0322) 0.0789 (0.1915) (0.1791) 0.9943 0.7881 α = 0.28 emp,0 wi,j α 0.02025 0.0349 (0.0375) 0.0047 (0.0097) (0.5814) 2.6422 (0.0028) 0.0064 0.1308 (0.02346) (0.1310) 0.1079 (0.0038) 0.0001 (0.0036) 0.0092 0.0065 (0.0033) (0.0331) 0.1118 (0.1734) (0.1611) 0.9878 0.7968 α = 0.28 = movi movj 0.02005 0.0247 (0.0379) 0.0062 (0.0099) (0.6192) 3.0981 (0.0031) 0.0052 0.1297 (0.02367) (0.1352) 0.0473 (0.0039) 0.0036 (0.0037) 0.0099 0.0077 (0.0033) (0.0354) 0.0792 (0.0641) 0.1637 (0.0393) 0.0367 α = 0.02 mov,0 wi,j = mig,0 wi,j α migi,j α = GDPi GDPj α 0.02145 0.0278 (0.0383) 0.0071 (0.0098) 2.9388 (0.6060) (0.0030) 0.0049 0.1299 (0.0253) 0.0562 (0.1349) (0.0039) 0.0035 (0.0036) 0.0096 0.0071 (0.0034) 0.0813 (0.0352) (0.0333) 0.0762 (0.0276) 0.0356 α = 0.1 GDP,0 wi,j t t t s t t tr ① t r s r st t s t ② t t r t s t t tr ① st t t t r t r r t r α, t α ③ s s r rt t s s t s t t st t s st t st ② s t t s t r s t ② rst s t st t r s t r t ② 0.02051 (0.0379) 0.0291 (0.0421) inc 0.0042 (0.0097) 0.0054 (0.5725) 2.5322 3.0193 (0.6507) (0.0028) 0.0046 (0.0032) 0.0051 (0.0029) unem pop Rent 0.1367 (0.0234) 0.1337 N HP I (0.0273) (0.1286) (0.1454) 0.1360 0.0806 (0.0038) (0.0035) UW I (0.0043) (0.0038) (0.0033) 0.0069 (0.0038) Starts (0.0339) 0.1060 (0.1466) 0.0830 Yt 1 (0.0380) 0.8988 0.8173 ρ (0.1565) 0.7098 (0.1397) α = 0.5 0.7353 = exp( αdi,j ) α = 0.35 t t W λ G,0 wi,j = G,0 wi,j d α i,j st t t s t tr ①

st t r s ts t t tr ① t r ts r t r rs t λ 0.4W G + 0.6W emp 0.5W G + 0.5W mov 0.2W G + 0.8W mov 0.1W G + 0.9W GDP αg = 0.35 αe = 0.4 αg = 0.45 αe = 0.15 αg = 0.55 αe = 0.25 αg = 0.55 αe = 0.35 0.8429 0.8964 0.9007 0.8038 0.9979 0.9988 0.9774 0.9984 0.0905 0.1084 (0.1644) ρ Yt 1 Starts Completed BP UW I N HP I Rent pop unem inc σ (0.1697) (0.0334) 0.0070 (0.1528) (0.1550) (0.1596) (0.1586) 0.0835 (0.0334) (0.0333) 0.0059 0.0073 (0.1735) (0.1831) 0.0747 (0.0335) 0.0070 (0.0032) (0.0033) (0.0032) (0.0031) 0.0080 0.0084 0.0078 0.0070 0.0013 0.0017 0.0008 0.0015 0.0987 0.1314 0.0870 (0.0033) (0.0037) (0.1299) 0.1377 (0.0037) (0.0033) (0.0038) (0.0040) (0.1273) (0.1286) 0.1337 0.1297 (0.0031) (0.0036) 0.0741 (0.1295) 0.1403 (0.0241) (0.02294) (0.0237) (0.0251) 0.0042 0.0050 0.0045 0.0038 (0.0029) 2.4379 (0.5707) 0.0051 (0.0094) 0.0029 (0.0028) (0.0028) 2.2804 2.6339 (0.5668) (0.5704) 0.0042 0.0046 (0.0096) (0.0093) 0.0385 0.0281 (0.0029) 2.6497 (0.5721) 0.0037 (0.0092) 0.0241 (0.0371) (0.0373) (0.0375) (0.0372) 0.01968 0.01984 0.01962 0.01949 t s t t st t s st t st ② s t t s t r s t ② s r s r t t st r r t W st t t t t t tr ① r ② t r st s r t s WN = g (di,j, zi,j, θ) r θ = (αg, αe, a) r t tr ① s t ② s s r t② s t ② s t r r t r αg r t tr ① t r r t r αe t s t t t r t r a s t s ② st t s ③ t

st t r s ts t t tr ① r t s t ① t t t ts s rs t s λ 0.8W G + 0.2W emp 0.9W + 0.1W mig 0.5W G + 0.5W mov 0.4W G + 0.6W GDP αg = 0.6 αe = 0.11 αg = 0.5 αe = 0.05 αg = 0.5 αe = 0.35 αg = 0.15 αe = 0.5 0.7607 0.8028 0.8977 0.8092 0.9693 0.9971 0.9973 0.9985 (0.1600) ρ Yt 1 Starts Completed BP UW I N HP I Rent pop unem inc σ (0.1770) 0.1147 (0.0337) 0.0062 (0.1624) (0.1542) (0.1785) (0.1590) 0.0920 0.1141 (0.0336) (0.0332) 0.0061 0.0074 (0.1721) (0.1807) 0.0729 (0.0336) 0.0074 (0.0033) (0.0033) (0.0032) (0.0031) 0.0077 0.0077 0.0075 0.0076 0.0024 (0.0038) 0.0023 (0.0038) 0.0004 0.0023 0.1250 0.1241 0.0876 (0.0034) (0.1273) 0.1434 (0.0023) (0.0033) (0.0037) (0.1268) (0.1281) 0.1416 0.1349 (0.0033) (0.0037) 0.0702 (0.1297) 0.1404 (0.0237) (0.0236) (0.0236) (0.0253) 0.0045 0.0045 0.0045 0.0038 (0.0028) 2.1436 (0.5637) 0.0056 (0.0096) 0.0382 (0.0028) (0.0028) 2.1415 2.5286 (0.5615) (0.5662) 0.0054 0.0056 (0.0096) (0.0093) 0.0383 0.0301 (0.0029) 2.6497 (0.5721) 0.0039 (0.0092) 0.0228 (0.0374) (0.0372) (0.0372) (0.0371) 0.02004 0.01990 0.01967 0.01958 t s t t st t s st t st ② s t t s t s r s t ② s r s r t t st r r t W st t t t t t tr ① r ② t r st s r t s WN = g (di,j, zi,j, θ) r θ = (αg, αe, a) r t tr ① s t ② s s r t② zi,j s t ② s t r r t r αg t r t t r r t r αe t t t t r t r a s t s ② st t s ③ t