Spatial basis risk and feasibility of index based crop insurance in Canada: A spatial panel data econometric approach

Transcription

1 Spatial basis risk and feasibility f index based crp insurance in Canada: A spatial panel data ecnmetric apprach Millin A.Tadesse (Ph.D.), University f Waterl, Statistics and Actuarial Science, Canada. mayten01@gmail.cm Outline Backgrund and mtivatin Thery A mdel f crp insurance pricing under spatial basis risk Panel data ecnmetric methd Data and results Cnclusin and plicy implicatins 1

2 Backgrund Basis risk in crp insurance literature cmmnly defined: Ptential mismatch between actual lss (yield, incme, etc) and a predetermined parameter (index) that trigger a lss (weather variable, NDVI, etc) (Mahuel 2001; Turvey 2001). When the mismatch is ften attributable t spatial differences, the term spatial basis risk is ften used. The prblem is unique t index based insurance (IBI) scheme that des nt require actual field lss assessment. Farmers face mst f the risks (e.g. receive n payut) when in fact they shuld have been paid but smetimes insurance agencies may pay farmers (when in fact they shuld nt). 2

3 Backgrund Key advantages f IBI: Reduce mral hazard and adverse selectin prblems Lw administrative csts Hwever, an emerging questin is t whm are the abve benefits? T farmers r insurers? In mst cases (at least in develped natins where access t credit and ther financial markets are relatively k),insurers are benefiting by mving twards IBI. The lack f clear benefit t prducers (cmpared t the traditinal crp insurance scheme including the existence f self-insurance mechanisms, gvernment subsidy, etc) and the relatively big spatial basis risk: Undermined the demand fr IBI even in areas with high level f subsidy (60% in Canada). Fr instance, nly 10% f frage acreage is insured in Canada until end f 2013 (Agricrp, 2013). 3

4 Mtivatin f this study Given the staggering lw demand in IBI and prevalence f spatial basis risk facing prducers, this paper aims: T examine the feasibility f IBI using a simple thery explaining the behavir f a typical frage grwer in Ontari, having tw insurance ptins (i.e. MPCI and IBI). IBI fr frage has been peratinal in Canada since 2003/2004. T develp methds t better quantify and reduce the prblem f spatial basis risk in IBI fr frage. 4

5 Thery: A mdel f crp insurance under spatial basis risk Assume a market with a single insurance prvider t N number f farmers. A typical farmer i in regin S has tw crp insurance ptins: Traditinal crp insurance (the term MPCI used here) that requires field lss assessment: Mral hazard and adverse selectin are cst t insurers but hidden benefit t prducers N basis risk t prducers IBI (n field lss assessment) But ptentially expse farmers fr spatial basis risk Maximizing expected utility f net incme requires cmparing the fllwing tw equatins: MPCI a E( U ( )) p y ( A, x, ) c( p, z ) (2 ) MPCI is is is is is is IBI E( U ( )) p y ( A, x, ) c( p,, z ) (2 b) IBI is is is is is is 5

6 Thery: A mdel f crp insurance under spatial basis risk If p MPCI and p IBI are equal, keeping ther factrs cnstant, participatin in MPCI prvides a psitive incme, EU ( ( )) Where as in equatin (2b), the farmer faces an additinal cst (basis risk), 0. and expected net incme declines by the same amunt, MPCI is EU ( ( )) is IBI 0. In equilibrium, the cst f spatial basis risk shuld be less than the price advantage a typical farmer might get frm IBI, i.e. MPCI IBI p p is. is Thus, increased demand in IBI shuld be driven by the magnitude f is insurers willing t cmpensate farmers such as thrugh reduced price, i.e. p IBI p MPCI. 6

7 Thery: Pricing crp insurance under spatial basis risk Frm abve we have, IBI * MPCI p p is 3 MPCI where p E( C yi ) f ( yi )( C yi ) ; 0 y i C (See Yeh and Wu, 1966). Under the nrmal curve thery with n basis risk, Btts and Bles (1958) expressed average premium per acre at time t as: T mt where At M i.e. prprtin f ttal acres with yields belw C; mt and M t are the number f t 1 acres belw the cverage and ttal acreage, respectively, at time t; Yit yi M t is the mean f acres yield ( y ) fr a particular year; the height f rdinate at is the standard deviatin f acres yield (where i MPCI T p A ( C Y ) d (4) t t t t d C; by is equal t a cnstant prprtin f lng term average yield, Y ) (Btts and Bles, 1958). 7 b i

8 Thery: A mdel f crp insurance under spatial basis risk Fllwing (Btts and Bles, 1958) and given lng term claim inf and actual payut, we can apprximate the standard deviatin f spatial basis risk by, and substitute int earlier frmula t get the ptimal premium under spatial basis risk: IBI * T p At C Yt dt ( ) (6) where λis with representing the prprtin f lng term spatial basis risk, λ is. 8

9 Ecnmetrics: Ratinale fr spatial dependence Main issues in supprt f spatial dependence analysis in agriculture (Nelsn 2002; Langyintu and Mekuria, 2008; Greene, 2008): Crp yield bservatins in ne lcatin is crrelated with its neighbring lcatin bservatins; Crp bservatins cllected in adjacent time perids are mre likely t be crrelated than yield bservatins separated in time; Thus, methds that allw spatial dependence are necessary (e.g. spatial dependence ecnmetrics methds such as by Anselin (1988). 9

10 Panel data ecnmetrics with spatial dependence Key limitatins f standard spatial ecnmetric methds: Rely either n purely crss-sectinal r time series data Lacks better identificatin strategies (fr endgenus regressrs) (Gibbns and Overman, 2012, Mstly pintless spatial ecnmetrics, JRS ). Linear fixed effects panel data mdel via cntrl functin apprach is advantageus (Wldridge 2002) and applied in this paper: Allws researchers t estimate and cntrl ( partial ut ) bth spatial and tempral dependences withut relying n bjectively determined spatial weighting matrix. Slves mst f the identificatin prblems that plague spatial ecnmetric mdels develped in 1980 s such as by Anselin (1988, 2006). Standard tests (and methds t crrect) fr serial crrelatins and heterskedascticity (fr panel data) are available and simple t implement 10

11 Linear fixed effects panel data with cntrl functin apprach: A tw step prcedure (Wldridge 2002) First stage: Ptentially endgenus variable is regressed using plausible instrument(s) and gd exgenus variables Predict and save residual (s) Secnd stage: Predicted residual frm the abve stage, the endgenus variable and additinal exgenus variables will be used t estimate cefficients (e.g. using linear fixed effects panel methd as used in this study). 11

12 Data and results 12

13 Table3: Impact f weather n frage yield in Ontari, Dept var: lg f frage yield (bus/acre) but fr first stage: daily ttal prcpt OLS regressin Cntrl functin: Linear fixed effects panel data GDD nly GDD & prcpt First stage Secnd stage: GDD nly Secnd stage: GDD& prcpt Ceff./(SE) Ceff./(SE) Ceff./(SE) Ceff./(SE) Ceff./(SE) April grwing degree days **** **** **** **** (0.01) (0.01) May grwing degree days June grwing degree days *** *** (Next page) July grwing degree days August grwing degree days *** * September grwing degree days **** *** *** ** April grwing degree days squared **** **** **** **** May grwing degree days squared * ** * June grwing degree days squared **** **** July grwing degree days squared August grwing degree days squared ** * September grwing degree days squared **** *** April precipitatin ** (0.00) (0.01) May precipitatin **** ** June precipitatin * July precipitatin *

14 Table3: Cntinued: OLS regressins Cntrl functin: Linear fixed effects panel data Dept var: lg f frage yield (bus/acre) but first stage dept var is daily ttal prcpt GDD nly GDD & RF First stage Secnd stage: GDD nly Secnd stage: GDD& RF Ceff./(SE) Ceff./(SE) Ceff./(SE) Ceff./(SE) Ceff./(SE) August precipitatin (0.00) (0.01) September precipitatin Residual sil misture, lagged precipitatin **** (0.02) April precipitatin squared May precipitatin squared *** June precipitatin squared July precipitatin squared August precipitatin squared September precipitatin squared Wind speed in km/hur **** (0.01) Altitude (mitted) Time trend (0.00) Quadratic time trend (0.00) Predicted precipitatin residual (deviatin) * Cnstant **** **** **** **** (0.01) (0.01) (34.81) (0.01) (0.01) Number f Obs Prb > chi Lg likelihd rati Adjusted R square Crr (u_i, Xb) rh (fractin f variance due t crss sectinal units) Mdified Wald test fr grup wise heterskedasticity Chi2(3)=1130**** Chi2(3)=1106**** Jint significance test (F-test) F(4,4015)=16.5**** F-test u_i:0=109*** F-test u_i:0=106****

15 Cnclusin and plicy implicatins 1. Fr increased IBI uptake, the gains frm reduced insurance premium under IBI shuld be greater than the cst f spatial basis risk plus sme hidden benefits t farmers (frm mral hazard and adverse selectin prblems) that may be lst by mving away frm the traditinal scheme. 2. Secnd, given actual yield lss (insurance claim) and payut prvided by insurers t farmers (acrss space and time), this study shws the ptimal per acre premium rate and a cnstant prprtin representing a lng term deviatin in spatial basis risk. 3. This paper applied a relatively simple ecnmetric methd t reduce the prblem f identificatin facing standard spatial ecnmetric methds. It challenges the exgeneity f rainfall in mdels estimating the relatinship between yield and weather. 4. It is shwn that a unit decrease in precipitatin in May, June and July results in 1%, 0.7% and 0.8%, respectively, reductins in frage yield. Thus, insuring farmers fr rainfall deficit fr these mnths is relevant. 15