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Evaluating the impact of climate change on Canadian Prairie agriculture Ayouqi Pourtafti, Hossein 2013

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Evaluating the Impact of Climate Change  on Canadian Prairie Agriculture   by Hossein Ayouqi Pourtafti  B.A.Sc., Sharif University of Technology M.Sc., Allameh Tabatabai University   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in The Faculty of Graduate and Postdoctoral Studies  (Agricultural Economics)  The University of British Columbia  (Vancouver)  September, 2013 ? Hossein Ayouqi Pourtafti 2013 ii  Abstract Climate change is a long-term shift in the average weather conditions that threatens settlements, societies, and industries. Agriculture is one of the most climate-sensitive industries since the production in this sector is highly dependent on various weather factors. The main objective of this study is to evaluate the economic impact of climate change on Canadian Prairie agriculture using the well-known Ricardian model. The Ricardian model is best described as a hedonic regression of farmland value on an assortment of climatic and non-climatic variables. This model is widely used in economic analysis because it captures farmers? adaptation strategies to climate change. To estimate the parameters of the Ricardian model, three methods are utilized: pooled weighted least squared (WLS), random effects, and spatial random effects. The estimated coefficients are used to predict the impact of three potential climate and price change scenarios on farmland value in the Canadian Prairies. The main contributions of this study relative to existing studies are: the use of updated data, the inclusion of expected prices rather than actual prices in the model, and the utilization of spatial econometrics methods to estimate the model. The estimated marginal impacts of climate demonstrate that an increase in rainfall and winter, spring, and fall temperatures will increase farmland value; the effect is opposite for July temperature. The signs of the marginal impacts of rainfall and July temperature reveal that water availability plays a very important role in crop production on the Canadian Prairies. Overall, climate change is predicted to increase the value of farm land on the Canadian Prairies by an average of 0.9% to 3.87% annually. However, the northern part of Saskatchewan and the north-eastern part of Alberta are forecasted to experience a decrease in farmland value under a medium climate change scenario. The current analysis predicts that farm welfare in the Prairies will increase by about $1.14 - $4.1 billion annually as a result of climate change. This suggests that with proper adaptations, climate change can be beneficial for Prairie agriculture.    iii  Preface This thesis is original, unpublished, independent work by the author, Hossein Ayouqi Pourtafti.   iv  Table of Contents Abstract?..? ......................................................................................................................... ii Preface??? ....................................................................................................................... iii Table of Contents .................................................................................................................. iv List of Tables.. ...................................................................................................................... vii List of Figures ...................................................................................................................... viii Acknowledgments ................................................................................................................. ix Chapter 1: Introduction ................................................................................................... 1 1.1. Background .................................................................................................................. 1 1.2. Problem Statement ....................................................................................................... 4 1.3. Objectives .................................................................................................................... 6 1.4. Methodology ................................................................................................................ 8 1.5. Outline ....................................................................................................................... 10 Chapter 2: Literature Review and Overview of the Canadian Prairies .................... 11 2.1. The Canadian Prairies ................................................................................................ 11 2.1.1. Socio-Economic Features ................................................................................... 12 2.1.2. Agriculture .......................................................................................................... 14 2.1.3. Climate Change .................................................................................................. 15 2.1.4. Impact of Climate Change on Agriculture ......................................................... 18 2.2. Literature Review ...................................................................................................... 19 Chapter 3: Theoretical Framework .............................................................................. 24 3.1. Production Function with Climate Factors ................................................................ 24 3.2. Ricardian Model ........................................................................................................ 26 3.3. Ricardian Model with Variable Output Prices .......................................................... 29 v  3.4. Adaptive Expectations ............................................................................................... 31 Chapter 4: Methodology ................................................................................................ 34 4.1. Variables .................................................................................................................... 34 4.1.1. Dependent Variable ............................................................................................ 34 4.1.2. Independent Variables: Climate Variables ......................................................... 35 4.1.3. Independent Variable: Dummy Variables .......................................................... 38 4.1.4. Independent Variables: Control Variables ......................................................... 38 4.1.5. Independent Variables: Market Price Variables ................................................. 38 4.2. Empirical Methods .................................................................................................... 39 4.2.1. Cross Section Approach ..................................................................................... 39 4.2.2. Panel Data Analysis ............................................................................................ 40 4.2.3. Potential Problems in Regression Analysis ........................................................ 45 4.3. Prediction ................................................................................................................... 47 Chapter 5: Empirical Analysis ...................................................................................... 48 5.1. Estimation Results ..................................................................................................... 48 5.1.1. Climate Variables ............................................................................................... 51 5.1.2. Grain and Cattle Prices ....................................................................................... 53 5.1.3. Control Variables ................................................................................................ 53 5.1.4. Dummy Control Variables ................................................................................. 55 5.1.5. Spatial Lag .......................................................................................................... 55 5.2. Comparing the Estimates with Other Canadian Studies ............................................ 55 Chapter 6: Prediction ..................................................................................................... 57 6.1. Climate Change Scenarios ......................................................................................... 57 6.2. Evaluating the Impact on Farmland Value ................................................................ 59 6.3. Comparing the Results with the Other Canadian Studies ......................................... 65 vi  Chapter 7: Conclusion .................................................................................................... 66 7.1. Summary .................................................................................................................... 66 7.2. Caveat ........................................................................................................................ 68 7.3. Recommendation for Future Studies ......................................................................... 70 Bibliography ?????????????????????????..????..72 Appendix: Stata printouts ..................................................................................................... 76     vii  List of Tables Table ?2.1: The Prairies Urban and Rural Population ........................................................... 12 Table ?2.2: Farms, Farm Area and Crop Productions, 2011 .................................................. 14 Table ?2.3: Crops Area and Number of Livestock, 2011 ....................................................... 15 Table ?2.4: Predicted Changes in Farmland Value, Reinsborough (2003) ............................ 22 Table ?4.1. Variables .............................................................................................................. 36 Table ?4.2: Summary of Variables ......................................................................................... 37 Table ?5.1: Weighted Least Square Estimation Results ........................................................ 49 Table ?5.2: WLS, Random effects and Spatial Random effects estimation results ............... 50 Table ?5.3: Marginal impact of climate variables (MIC) ....................................................... 52 Table ?5.4: The Correlations between Error Terms and Climate Variables .......................... 53 Table ?6.1: Summary of SRES A2 Emissions Scenario ........................................................ 58 Table ?6.2: Climate Change Scenarios for the Prairies .......................................................... 59 Table ?6.3: Average Annual Change in the Prairies Farmland Value ................................... 61 Table ?6.4:?Annual?Change?in?the?Prairies??Farmland?Values?(Farm?Welfare), .................... 62 Table ?6.5: Average Annual Change in the Prairies Farmland Value (No Price Change) .... 62 Table ?6.6: Annual Change in the Prairies??Farmland?Values, No Price Change .................. 63   viii  List of Figures Figure ?2.1: The Prairies Ecozone ......................................................................................... 11 Figure ?2.2:?Canada?and?the?Prairies??GDP?by?Provinces ...................................................... 13 Figure ?2.3: Climate Normals for the Prairies (1961-1990), Temperature ............................ 16 Figure ?2.4: Climate Normals for the Prairies (1961-1990), Precipitation ............................ 17 Figure ?2.5: Annual Mean Temperature Change (?C) ........................................................... 17 Figure ?2.6: Annual Mean Precipitation Change (%) ............................................................ 18 Figure ?3.1: The Process of Adaptation ................................................................................. 25 Figure ?3.2: Welfare impact of climate change ..................................................................... 29 Figure ?3.3 : Direct and Indirect Effects of Environmental Factors on Profit ....................... 29 Figure ?3.4: Supply Reduction Effects .................................................................................. 30 Figure ?3.5: The Impact of Price in Adaptation Process ........................................................ 31 Figure ?3.6: Compare Expected Price to Current Price of a Hypothetical Commodity ........ 32 Figure ?6.1: Modeled climate data between 2011-2099 ........................................................ 60 Figure ?6.2: The percentage change in Farmland value ? RE model ? Medium Scenario .... 63 Figure ?6.3: The percentage change in Farmland value ? RE model ? Strong Scenario ....... 64 Figure ?6.4: The percentage change in Farmland value ? RE model ? Extreme Scenario .... 64  ix  Acknowledgments I would like to express my deepest gratitude to my supervisor, Prof. James Vercammen, for his excellent guidance, patience and providing me with an opportunity to pursue my education in the field of my interest. A special thanks goes to my parents, who love and support me throughout my whole life. Finally, I would like to thank my wife, Neda, cheering me up and stood by me through the good times and bad. 1  Chapter 1: Introduction 1.1. Background Climate change is defined as significant and lasting changes in the mean and/or variability of climate properties like temperature, precipitation, humidity, solar radiation, and wind speed (Schmidt and Wolfe, 2009). This phenomenon could be the result of a long-term natural cycle and human activities; however, most scientists believe that the contribution of the latter one is considerably larger than the former (George, 2011). Expanding the emission of greenhouse gases including: water vapour, carbon dioxide, methane, nitrous oxide, and CFCs is recognized as the root cause of climate change (Pachauri, 2007). In recent decades, serious concerns have arisen over the effects of climate change, and extensive studies have been done to evaluate these effects. The negative impact of climate change on natural systems related to: snow, ice and frozen ground; terrestrial, marine, and freshwater biological systems; hydrological system; human health and activities; forestry and agriculture have been observed by scientists with noticeable confidence (Pachauri, 2007). Since agriculture is highly sensitive to the states of climate, assessing the effect of climate change on this sector is an important topic for researchers. Many studies focused on the relationship between climate change and agriculture. Some researchers have examined the effects of agricultural activities on climate change, and some have worked on the impact of climate on agriculture ___ the present study belongs to the latter category. The negative effects of climate change on agriculture come through changes in the mean and variability of precipitation and temperature, water availability, and the appearance of new diseases (Fischlin et al., 2007). Climate change can affect livestock and crop productivity and consequently it affects food prices and farmland values.  Production functions were first used to examine the effects of climate change on agriculture. This approach, however, overestimated the damages of climate change since it did not take adaptations into account. In fact, faced with the climate challenges, farmers adapt to changes to alleviate the negative effects and in some cases even benefit from the new situation. Land-use switching, changing seeding times, irrigation methods, and 2  fertilization applications are examples of adaptation that may be employed by the producers (Brklacich et al. 1997; Mendelsohn et al. 1994). Therefore, contrary to what is expected, it is possible that not only are farmers not harmed by climate change, but they also may benefit from it. In other words, although some types of adaptations like technological development and financial management are costly at first, the benefits of such adaptations could exceed the costs in the long-term. Other reasons which make climate change beneficial include profiting from other countries faced with climate change, and benefiting from supportive government policies (Wreford, 2010). This argument shows the importance of including the adaptations in economic modeling to explain the actual impact of climate change.  As expected, the effects of climate change on farmland value vary over regions. Studies in the US show that climate change will generally harm the agricultural economy while the Canadian analyses suggest a positive impact on agriculture. Although almost all research for a specific region have forecasted the same direction for climate change impacts, the magnitude of the predicted effects vary significantly across studies. For example, Reinsborough (2003) predicted a 0.9 to 1.5 million dollar benefit for the Canadian agriculture due to climate change while Weber and Hauer (2003) suggested a 5.4 billion dollar annual increase in agricultural GDP. The difference in predictions could partially be due to using dissimilar regional scale and also to using different climatic and non-climatic variables. In the current study, an economic model is utilized to estimate the impact of climate change on Canadian Prairie agriculture. The Prairies was chosen to be the study area since it has unique and important socio-economic and agricultural characteristics. The Canadian Prairies is a vast area stretched between Ontario and British Columbia and divided into three provinces (Alberta, Manitoba, and Saskatchewan). This region has an area of 1.78 million km2, with a population of 5.9 million in 2011, corresponding to 20% of and?18%?of?Canada?s?area and population, respectively (Census of Canada, 2011). The Prairies also represents 47% of farms, 81% of farm area and 58% of crop production in Canada. The main crops in the Prairies are wheat, canola, alfalfa, and barley which have a very large share of the?Canada?s?production; 98% of canola, 94% of wheat, 93% of barley, and 76% of alfalfa in Canada are 3  harvested in the Prairies (Census of Agriculture, 2011). Thus, any effects of climate change on the Prairies agriculture would be a meaningful change for all Canada. The climate in the Prairies region is mainly sub-humid and cold since it lies in the rain shadow of the Rocky Mountains and in mid-latitudes (Diaz et al. 2010). Historical observations show several changes in the Prairies climate: the mean temperature has risen by 1.6?  ?C since 1985; the snow cover season has shortened; and the number of days with the temperature above 30? ?C has surged (Wheaton et. al, 2010). The latest drought in the region, which happened in 2001-2002 and could very well be the result of climate change, had a serious impact on crop production. Over that time period net farm income dropped by about 1 and 2.3 billion dollars, in 2001 and 2002, respectively. A number of studies have predicted future climate trends for the Prairies. For example, a greater frequency of severe drought and flooding, as an extreme result of climate change, was predicted by Kharin et al. (2007). Nakicenovic et al. (2000) drew scatterplots of predicted changes in mean annual temperature, and precipitation for the 2020s, 2050s, and 2080s. Although almost all predictions suggest an increase in the mean temperature, there are different opinions about future precipitation. Barrow (2010) predicted a decrease of between 0% and 10% in the annual mean precipitation in most parts of the Prairies. This finding is in contradiction with the forecasts of Environment Canada (2010) and Nakicenovic et al. (2000), both of which predicted an increase in precipitation. To sum up, there are two main reasons for choosing the Prairies as the study area: 1) this region has a dominant share in the Canadian agriculture and agri-food system; and 2) the Prairies are known to be vulnerable to climate change.  Although climate change is undoubtedly affecting agricultural activities on the Prairies, quantifying the impacts of climate change will help decision-makers and producers implement more appropriate policies and practises to deal with the impacts. The design of national agricultural and environmental strategies should be rigorous and certainly should be based on careful predictions about the potential advantages and disadvantages of climate change for Canadian agriculture. 4  1.2. Problem Statement  The gold standard method of analyzing the impact of climate change on agriculture is the Ricardian model, which was developed by Mendelsohn et al. (1994). The Ricardian model has been widely used to estimate the effect of climatic and non-climatic (e.g. geographical and socio-economic) variables on the net value of agricultural production. Mendelsohn?s approach is based on a hedonic modeling of farmland pricing where farmland value is defined as the dependent variable. Mendelsohn?s model is well suited to take farmers? adaptation to climate change into account. Indeed, under competitive markets, farmland rent is a measure of the net profits of the best use of the land and, of course, adaptation is reflected in the best use of the land. Thus, as opposed to the traditional approaches which were based on empirical production functions, the Ricardian model considers future land management (including the adaptation to climate change) as well as present practises. The Ricardian model, often?with?modifications? to? improve? the?model?s?predictive?ability, has been applied to a variety of countries and regions to assess the agricultural impacts of climate change (Mendelsohn and Dinar 2009). The Ricardian model has delivered consistent results and it is this consistency which probably best explains the model?s?popularity. Several different modifications of the standard Ricardian model have been used to examine the relationship between agriculture and climate change. In the early studies, following the standard Ricardian approach, cross section data were used to estimate the climate impacts with the assumption of fixed market prices (e.g. Reinsborough, 2003 and Mendelsohn et al., 2007). More recent studies have used panel data rather than cross section data to estimate the Ricardian model (Amiraslany, 2010 and Massetti et al., 2012). Similarly, early panel studies assumed the prices of commodities are fixed over time. In more recent studies the fixed price assumption has been relaxed (Amiraslany, 2010). The most recent attempt to estimate the Ricardian model for the Canadian Prairies was Amiraslany (2010). This study provided an excellent advancement in the economic analysis of climate change and it is sure to be a Canadian benchmark for future research. There are several reasons why this thesis continues to examine the economic link between climate change and agriculture on the Canadian Prairies. First, more updated data is available to 5  estimate?the?Ricardian?model.?Second,?Amiraslany?s?(2010)?list?of?commodities?which?were?included?in?the?analysis?was?somewhat?limited.?Third,?although?Amiraslany?s?(2010)?relaxed?the fixed price assumption, additional improvements in the way that commodity prices are incorporated into the model are possible. Finally, one particular assumption that underlies Amiraslany?s?(2010)?econometric?model? is?somewhat?questionable?and?so?improvements in this regard are also possible. Each of these reasons is now explained in greater detail. With respect to using updated data, given the importance of climate change, re-estimating the model with updated data is probably sufficient justification for additional research. Indeed, as climate change progresses, and previous Canadian studies become outdated, it is highly worthwhile to re-estimate the model using the new data in order to capture the possibility of changes in the marginal effects over time due to the new adaptations against climate change. Regarding? commodity? coverage,? Amiraslany?s? (2010)? analysis? included?prices of only the two major crops ___ wheat and canola. Excluding the price of livestock and other agricultural commodities is likely to result? in? biased? estimates? of? the? model?s?parameters. The accuracy of the Ricardian model can likely be improved significantly by including in the econometric model the prices of a more comprehensive list of agricultural commodities from the Canadian Prairies.  With respect to fixed versus variable prices, Amiraslany (2010) showed that assuming a fixed price over time when estimating a model with panel data will typically result in biased estimates?of?the?model?s?parameters.?As?an?alternative,?Amiraslany?s?(2010) incorporated the prevailing market prices for commodities for each census year rather than assuming a single price for each commodity across time. Although utilizing updated absolute market prices for the census years is a major improvement over the fixed price assumption, this revised approach can still result in biased estimates. Indeed, if a sharp price change happens just before a census year, the impact of commodity price on agricultural land values will certainly be misestimated. What is needed is? a? proxy? for? farmers?? expectation? of? future commodity prices because it is these expectations which largely determine the market value of farmland.  Finally, regarding the econometric analysis of panel data, Amiraslany (2010) assumed that the climate normals have changed over 1991-2001 and therefore fixed effects regression 6  techniques could be used to estimate the coefficients of the climate variables. Massetti and Mendelsohn (2012) used 1971-2000 climate normals for all census years because they believe that the actual change in the climate change normals over one or two decades will be essentially zero from an estimation perspective. Since in the case of time-invariant climate variables the fixed effects method is unable to estimate all coefficients, Massetti and Mendelsohn (2012) used a two-stage method (introduced by Hsiao, 2003) to estimate the coefficients of the time-invariant climate variables (this two stage method is a special type of fixed effects procedure). The two-stage model is one way to estimate the model with time-invariant climate variables; however, we will argue below that superior methods which account for spatial correlation are available and should be used.  To summarize, the previous benchmark Canadian study of climate change (Amiraslany, 2010) is currently out of date and the assumptions which have been made about which commodities to include is somewhat restrictive. Moreover, although this study made important improvements by allowing the commodity prices to vary over time when panel data is used, the inclusion of current market prices for commodities rather than a proxy measure? of? farmers?? expected? future market prices is still? limiting.? Finally,? Amiraslany?s assumption that climate change normal variables vary over time is controversial.  1.3. Objectives The main goal of this study is to extend the analysis of Amiraslany (2010). Specifically, a modified Ricardian model with up-to-date and more comprehensive data and spatial econometric techniques is used to estimate the economic impact of climate change on the welfare of farmers in the Canadian Prairies. As discussed above, the standard Ricardian model is essentially a hedonic regression of farmland value on a variety of climatic and control variables. In the Ricardian model, farmland value serves as the dependent variable, since, not only does it capture the adaptations strategies against climate change but it also serves as a reasonable proxy measure for farm welfare. Following Amiraslany (2010), we estimate the climate change impact using panel data rather than cross section data. By using panel data, we have more data points for each region and also we can consider fixed region and time effects in the estimation. This approach also 7  captures unobservable factors that affect the dependent variable over time and across regions. Estimating the panel model with updated data is an important objective of the current analysis. Amiraslany (2010) used 1991, 1996 and 2001 census data. We have added 2006 and 2011 census data to the dataset in order to generate more up-to-date results.  Recall that Amiraslany (2010) included the prices of only wheat and canola in his dataset when estimating the Ricardian model. We include the four most cultivated grains in the Prairies: wheat, canola, alfalfa, and barley. In addition, the price of cattle is included as a representative for animal farms. Also recall that Amiraslany (2010) relaxed the fixed price assumption by including the current year commodity price rather than a singled fixed price in the panel dataset. In the present study, rather than including the current market price as an explanatory variable in the panel data, a proxy for expected price is used in the econometric model. As will be explained in greater detail below, farmers are assumed to have adaptive price expectations, as first proposed by Cagan (1956) and Nerlove (1958). This assumption implies that the current price of land will depend on both past and previous commodity prices rather than just current commodity prices.  To estimate the panel data model, three alternative econometrics approaches will be used: (1 pooled weighted least squares; (2 standard random effects estimation; and (3 spatial random effects estimation. The pooled model is common in mainstream Ricardian analysis with cross sectional data. Using the random effects assumption rather than the fixed effects assumption involves a trade-off. In? general,? the? fixed? effects?method? is? ?safer?? because? it?automatically addresses the problem of omitted variable bias. However, it is not possible to estimate the coefficients of variables which do not vary over time using the fixed effects method. Amiraslany (2010) assumed that long term climate variables changed over time and in doing so was able to use the fixed effects method to estimate the coefficients of the long term climate variables.  The approach used in this study is to assume that long term climate variables are fixed over time. This assumption precludes the use of fixed effects estimation and so random effects estimation must be used. The random effects assumption is only appropriate if one is confident that variables omitted from the regression equation are not correlated with the 8  climate variables. A previous study (Massetti and Mendelsohn, 2012), which was reluctant to use the random effects assumption because of a concern over omitted variable bias, chose to assume fixed effects and to use a two stage procedure to recover the coefficients of the time invariant variables, which included long term climate normal. In Chapter 4 we show that for the current analysis the random effects method is more appropriate than two-step fixed effects method because there is no evidence that omitted variables are correlated with the climate variables.  After estimating the Ricardian model by the three methods that were discussed above, we calculate the marginal effects. Knowledge of the marginal effects allows us to predict changes in the farmland value under alternative climate change and price change scenarios. To implement the climate and price change scenarios, forecasts will be borrowed from other relevant studies.  1.4. Methodology As previously noted, the analysis in this study is based on the Ricardian model which was introduced by Mendelsohn et al. (1994). In this model, the value of farmland serving as the dependent variable is regressed on climatic and non-climatic (socio-economic and dummy) variables to estimate the impacts of the climate variables. By introducing farmland value as the response variable, the model can capture the adaptation strategies which producers utilize in response to climate change. As was explained above, the value of adaptation strategies are reflected in farmland values because farmland rent represents the net profit of the best use of the land. Moreover, because the farmland value is the capitalized stream of the future profit from the farm, we can use farmland value to measure the change in the farm welfare which can be attributed to climate change.  In addition to adding updated data in the analysis, the price of more grains (wheat, canola, alfalfa and barley) and cattle are included in the model. The farm product price index is used to calculate the market price of the representative crop in each region. Lagged prices are incorporated in the model to reflect the inclusion of adaptive price expectations.  9  As well as the market  price, various socio-economic and dummy variables are included in the model to control for non-climatic impacts on farmland prices. The control variables in the current model are regional farm income, government transfers, population, soil type, and distance to the nearest highway and export terminal. Data on climatic variables are extracted from the 1971-2000 climate normal database. These variables include annual mean temperature and precipitation. Moreover, an evapotranspiration proxy is introduced as a climate variable to reflect the interaction between the temperature and precipitation. To estimate the model, panel data built from five census years will be used (1991, 1996, 2001, 2006 and 2011). The spatial unit of analysis is Census Sub-Division (CSD). According to Statistics Canada, Census Subdivision (CSD) is: ?The general term for municipalities (as determined by provincial/territorial legislation) or areas treated as municipal equivalents for statistical purposes.? There are more than 1500 CSD in the Canadian Prairies; however, only about 500 of them are rural areas which can be used in the current analysis. The socio-economic data is extracted from Canada Census of Population which of course varies over both time and region. Dummy and CSD characteristic variables are fixed over time but they vary over regions. Since climate change is a long-term phenomenon, to obtain the climate normals for each CSD, we assume that the climate variables are fixed over the considered time?interval and we use the 1971-2000 climate normals of the weather stations, which were released by Environment Canada. As the model contains time-varying variables (e.g. population and income) and time-invariant variables (e.g. climate normals), we need to employ appropriate estimation methods so that the coefficients of the both types of variables can be obtained. Regarding the econometrics approaches, since we use panel data, two methods can be used to estimate the model. The first approach is to pool the entire data set and then estimate the model in a single stage. The second approach improves on the pooling method by explicitly accounting for the variation over time of the key variables within the model. As previously 10  discussed, the standard random effects method is used to address the problem of estimating the model with time invariant climate variables. The formal econometric analysis concludes with a third estimation method. Specifically, we employ a spatial random effects approach in which the degree of dependency of farmland value amongst CSDs expliticly considered in the model in order to obtain a more accurate set of results. After estimating the model, we calculate the marginal impacts of climate change and then predict the impact of the potential climate change scenarios on farmland value and farm welfare. In our analysis, we will incorporate the climate change scenario for the Canadian Prairies which was forecasted by several earlier studies. We also include the price change scenarios in our analysis in order to have a more accurate prediction regarding what lies ahead for Prairie agriculture.  1.5. Outline The rest of the research is organized as follows. In chapter 2 the Canadian Prairies region is introduced and the relevant literature is reviewed. Also include in Chapter 2 are the results of the main land-climate Ricardian models which have previously been estimated for Canada. In chapter 3, the conceptual framework of the Ricardian model is described. Included in this discussion is the necessity of incorporating market prices and lagged prices into the model. Chapter 4, which focuses on the empirical methodology, describes the variables and econometrics procedures which were utilized in the analysis. In chapter 5, the coefficients of the model are estimated using the three different econometric methods. After presenting the estimated coefficients the marginal impacts of climate variables on the farmland value are calculated for each method. In chapter 6, using the three sets of estimated coefficients, the future farmland values in the Prairies are predicted under the three different climate and price scenarios. Finally, the summary and conclusion of the study are presented in chapter 7. 11  Chapter 2: Literature Review and Overview of the Canadian Prairies  2.1. The Canadian Prairies The Canadian Prairies is a vast area stretched between Ontario and British Columbia and divided into three provinces: Alberta, Manitoba, and Saskatchewan. According to the Terrestrial EcoZones of Canada, 25% of the Prairies provinces are occupied by the Prairie Ecozone (The shaded area in Figure ?2.1). The Prairies is known as the heartland of agriculture and industry and also the most broadly modified region in Canada ? the most parts of original wetlands and grass prairie in this region have changed over time (Prairie Adaptation Research Collaborative, 2008).  Figure ?2.1: The Prairies Ecozone  Source: Environment Canada In the Canadian agricultural studies, the Prairies area is the first region of interest because of its special characteristics. Although large cities now have their own share in this area, the rural?life?is?still?an?important?part?of?the?region?s?character.?Farming remains one of the main occupations and the main source of income for many of the residents1. According to the 2011 Census of Agriculture, 47% of the farms and 81% of the farm area in Canada are in the                                                  1. J.J. McCullough, The Canadian Prairies, Retrieved April 2013 from www.thecanadaguide.com.  12  Prairies. The strong dependence on primary production and also the climate characteristics show that the Canadian Prairies is more vulnerable to climate change than any other regions in Canada (Diaz et al, 2010). This region, therefore, would be a perfect case to assess the economic effects of climate change on agriculture in Canada.  2.1.1. Socio-Economic Features  The Canadian Prairies has an area of 1.78 million km2, with a population of 5.9 million in 2011, corresponding to 20% and? 18%? of?Canada?s? area and population, respectively. The historical census data shows that the Prairies population has increased by 70% over the last 40 years. This growth has happened mainly in urban rather than rural areas. Table ?2.1 shows that the population of rural area has surged only by 10% and its share of total population has declined from 49% in 1971 to 28% in 2011 (Census of Canada, 1971-2011).  Table ?2.1: The Prairies Urban and Rural Population  Population Urban Rural Urban Rural  number % of total population 1971 3,542,360 2,373,325 1,169,030 67 49 1976 3,780,865 2,604,980 1,175,885 69 45 1981 4,232,278 3,021,370 1,210,908 71 40 1986 4,438,455 3,264,805 1,173,650 74 36 1991 4,626,423 3,441,465 1,184,958 74 34 1996 4,800,961 3,570,056 1,230,905 74 34 2001 5,073,323 3,839,517 1,233,806 76 32 2006 5,406,908 4,149,686 1,257,222 77 30 2011 5,886,906 4,595,099 1,291,807 78 28 Source of Data: 1971-2011 Census of Canada  According to the provincial data, the mentioned population growth and distributions are uneven over provinces. The population of Alberta has increased dramatically while the populations in Manitoba and Saskatchewan have been almost motionless. Although the share of rural populations has decreased in all three provinces, the urban-rural population shifts are different in each province. While the rural populations of Alberta and Manitoba have increased by 42% and 10%, respectively, the Saskatchewan rural population has decreased by 20%. Statistics Canada (2009) has predicted that in 2036 the Canadian Prairies population 13  will reach 7.1, 7.7 and 8.4 million based on low, medium and high growth scenarios, respectively. In 2011, the Gross Domestic Product (GDP) of the Prairies was $426 billion which contributed to about 25% of Canada?s GDP. Besides, per capita GDP in this region was around $70,000 which is more than per capita GDP in Canada ($51,000). This wealth, however, is not shared equally over all provinces.? Per capita GDP in Alberta is $78,000 which is more than Saskatchewan and Manitoba with $71,000 and $45,000, respectively (Statistics?Canada,?2011).?The?Alberta?s?growing?oil-based economy is the main reason for the high share of this province in GDP and population growth in the Prairies (Kulshreshtha and Diaz, 2010). Figure ?2.2 shows?the?share?of?each?province?in?the?Canada?s?and?Prairies??GDP. Figure ?2.2: Canada and the Prairies? GDP by Provinces   Source of Data: Statistics Canada, 2011 For the Prairies, the primary resource sectors had a contribution of around 22% of GDP in 2012. Since some of these sectors (e.g. agriculture) are highly dependent on weather conditions, climate change can have a significant impact on the economy of the region. The  Alberta 69%  Saskatchewan 18%  Manitoba 13% The Prairies' GDP by Province, 2011  Ontario 37%  Quebec 20%  Alberta 17%  British Columbia 12%  Saskatchewan 4%  Manitoba 3% The rest 7% Canada's GDP by Province, 2011 14  service and public administration sectors also make a considerable contribution in the Prairies? GDP (Statistics Canada - CANSIM).  2.1.2. Agriculture The Prairies agriculture is placed in the Western Interior Basin 1  and it includes the northernmost part of the Great Plains of North America (Venema, 2006). According to 2011 Census of Agriculture, the number of farm operators in the Prairies is more than 133,000 which is 45% of all Canadian farm operators. This area represents 47% of farms, 81% of farm area and 75% of crop production in Canada (Table ?2.2).  Table ?2.2: Farms, Farm Area and Crop Productions, Canada and the Prairie Provinces, 2011  Number of Farms Area (acres) Production (metric tons) Manitoba 15,877 18,023,472 15,614,200 Saskatchewan 36,952 61,628,148 59,491,200 Alberta 43,234 50,498,834 55,938,300 Prairies 96,063 130,150,454 131,043,700 Canada 205,730 160,155,748 174,017,800 Source of Data: 2011 Census of Agriculture According to 2011 Census of Agriculture, the main crops in the Prairies are wheat, canola, alfalfa, and barley which are cultivated in 32%, 28%, 12%, and 9% of all the Prairies croplands area, respectively. These crops also have a huge share?of?the?Canada?s?production?? 99% of canola, 94% of wheat, 93% of barley, and 76% of alfalfa fields in Canada are located in the Prairies. Regarding livestock production, more than half of cattle and calves, 42% of pigs and 34% of sheep and lambs are raised in this region (Table ?2.3).  The mentioned data confirms that any effect of climate change on the Prairies agriculture would be a meaningful change for all Canada. Therefore, assessing the agricultural impact of climate change in this region seems to be vital for policy makers in order to prevent the problems?in?Canada?s?food?supply?systems.                                                  1. A physiographic region located in North America 15  Table ?2.3: Crops Area and Number of Livestock, Canada and the Prairie Provinces, 2011  Wheat (hectares) Canola (hectares) Alfalfa  (hectares) Barley (hectares) Cattle and Calves Sheep and Lambs Pigs Manitoba 1136122 1330847 533569 195638 1210568 63162 2850581 Saskatchewan 4824526 3957339 1450999 943478 2647372 113350 1028530 Alberta 2712892 2457147 1479981 1460960 5104605 202903 1397534 Prairies 8673540 7745333 3464549 2600076 8962545 379415 5276645 Canada  9257819 7838354  4544662  2787754  12789965 1108574 12679104 Source of Data: 2011 Census of Agriculture 2.1.3. Climate Change The Prairies region lies in the rain shadow of the Rocky Mountains and in mid-latitudes. The climate is mainly sub-humid with cyclonic storms, cold and long winters, and warm and short summers (Diaz et al. 2010). Temperatures in this region are highly related to latitude and altitude?temperatures progressively decrease as latitude and altitude increase (Figure ?2.3). Precipitation increases lightly from south to north and more considerably from west to east (Figure ?2.4). The combination of mentioned precipitation and temperature gradients has introduced a set of climatic zones from cool semi-arid to cold sub-humid which lies from southwest to northeast (Acton et al. 1998). Historical observations show several changes in the Prairies climate. The mean temperature has risen by 1.6? ?C since 1985; the snow cover season has decreased; the frost-free season has become longer; the temperature in winter has increased over the 1953-2005; and the number of days with the temperature above 30? ?C has surged (Wheaton et. al, 2010). To evaluate the impact of climate change on agriculture, some knowledge about the plausible future status of the Prairies? climate is needed. Climate predictions for the Prairies made by Environment Canada and other studies suggest that the above-mentioned trends will continue in the future. For example, a greater frequency of severe drought and flooding, as an extreme result of climate change, was predicted by Kharin et al. (2007). Nakicenovic et al. (2000) prepared scatterplots of predicted changes in the mean annual temperature and precipitation for the Prairies in which generally an increase in average temperature and precipitation are forecasted for the 2020s, 2050s, and 2080s. While almost all predictions suggest an increase in the mean temperature, there are different 16  forecasts for precipitation. For example, Barrow (2010) predicted a decrease between 0% and 10% in the annual mean precipitation in the most parts of the Prairies which is in contradiction with the predictions of Environment Canada (2010) and Nakicenovic et al. (2000). Figure ?2.3: Climate Normals for the Prairies (1961-1990), Temperature  Source: From impacts to adaptation: Canada in a changing climate 20071 Regarding the prediction methods, General Circulation Models 2  (GCMs) are the most commonly?used?models?for?specifying?climate?change?scenarios.?GCMs??equations?are?based?on the physical laws of energy, mass, moisture, and conservation. CCC-GCMII3  (1990) designed by Environment Canada is an example of using GCMs to provide climate change scenarios.                                                   1. Figure ?2.3, Figure ?2.4, Figure ?2.5, and Figure ?2.6 are copies of an official work that is published by Natural Resources Canada and that the reproduction has not been produced in affiliation with, or with the endorsement of, Natural Resources Canada. 2. Also known as General Climate Models 3. Canadian Climate Centre Second-Generation General Circulation Model 17  Figure ?2.4: Climate Normals for the Prairies (1961-1990), Precipitation  Source: From impacts to adaptation: Canada in a changing climate 2007  Figure ?2.5: Annual Mean Temperature Change (?C)  Source: From impacts to adaptation: Canada in a changing climate 2007  18   Figure ?2.6: Annual Mean Precipitation Change (%)  Source: From impacts to adaptation: Canada in a changing climate 2007  The? Government? of? Canada? has? published? a? report? titled? ?From? Impacts? to? Adaptation:?Canada?in?a?Changing?Climate?2007?. The report has plotted the change in precipitation and temperature for three scenarios (minimum, Median and Maximum) in the 2020s, 2050s, and 2080s using AOGCM 1 . According to these scenario maps, the largest increases in temperature and precipitation are predicted to occur in the north and east (Figure ?2.5 and Figure ?2.6) 2.1.4. Impact of Climate Change on Agriculture The Prairies region has one the most significant agricultural resources in the world; however, it is vulnerable because of the scarce water resources and climate variability. The Prairies climatic characteristics include: dominant air mass; temperature, precipitation and                                                  1. Atmosphere-Ocean General Circulation model  19  wind patterns; high flood risk; fire frequency; and severe droughts have made the agriculture of this region vulnerable against climate change (McGinn, 2010).  Climate change can affect agriculture industries directly and indirectly. The direct impact is through bio-physical changes which affect the agriculture supply chain, whereas the indirect one depends on the effect of climate change on agriculture in the rest of the world which may change demand for agricultural products (Diaz et al., 2010). According to all climate scenarios, the Prairies will face an increase in temperatures with a decrease in soil moisture. There is no unique scenario for precipitation; however, in either scenario, surging temperature increases the evaporation and as a result diminishes the soil moisture. Agricultural productions may show different response to the mentioned scenarios. For example, increasing temperature would lengthen the growing season which leads to a shorter required time for spring wheat to become mature and consequently earlier planting and harvesting (Brklacich, et. al., 1994). Livestock death rate, as another example, may increase because of hot weather or low quality water in the Prairies. Moreover, changing insects and arising new diseases are the other results of climate change that can affect both crops and livestock productions (Diaz et al., 2010). For a real example of the climate change impacts, the latest drought in the region, as an extreme sequence of climate change, in 2001-2002, had a serious impact on crop productions. The net farm income dropped by about 1 and 2.3 billion dollars in 2001 and 2002 respectively (Wheaton et al., 2005). 2.2. Literature Review In 1980's and early 1990's, scientists had studied the impact of greenhouse gas emissions on agricultural production by using traditional production functions. In this approach, they considered temperature, precipitation and pollutants as inputs and then made changes in them to estimate the impacts on production. However, the results usually showed a severe decrease in agricultural productions as a result of climate change. Mendelsohn et al. (1994) explained that the main reason of these overestimating damages is overlooking the adaptations that might be made by producers in response to the climate and economic changes. For example, switching to new crops and changing in land use and technology were some of the 20  adaptations which were omitted in the traditional production function approach. Furthermore, the production approach only works for regions that have similar physical properties and it is not valid for large-scale interregional comparisons (Weber and Hauer, 2003). To eliminate the above-mentioned drawbacks of production function technique, Mendelsohn et al. (1994) introduced the Ricardian approach in which instead of examining the effects of climate change on yields of different crops, the impact on the farmland net values and net revenue were studied. This study estimated the contribution of several climatic and non-climatic variables in the lower 48 states in the US. They used 2,933 cross-sectional observations to estimate two different models: cropland model and crop-revenue model. The results from the cropland model show a loss of between 6 to 8 billion dollars per year from given warming ranges, while the crop-revenue model suggests an annual gain of 1to2 billion dollars. They also extended their model through applying the aggregate farmland value for each county (1996), and adding the daily temperature variation, and the inter-annual temperature and precipitation as new variables in the model (1999). The Ricardian model has been applied in more than 27 countries (e.g. Canada, Mexico, Spain, Sri Lanka, Ethiopia, India, and China) (Mendelsohn and Dinar 2009). However, the literature on the Ricardian technique shows a variety of approaches, 1) using different climatic and non-climatic variables, 2) considering different climate change scenarios, 3) employing different empirical methods, and 4) applying the model in different spatial units are some of the efforts to extend the original model. In some papers, authors applied Ricardian model to multiple countries. For example, using data from eleven African countries, Kurukulasuriya and Mendelsohn (2011) introduced a structural Ricardian model in which the effects of climate change on irrigation choice and conditional income were evaluated. As another sample, Niggol and Mendelsohn (2008) used a Ricardian analysis for seven South American countries.  Moreover, Mendelsohn and Reinsborough (2007) compared the agricultural Ricardian analysis between the United States and Canada. For this purpose, they estimated three regressions with the same variables in which they considered: 1) the same climate response for both countries, 2) a different climate response, and 3) a different climate response for 21  only drylands. According to the first regression, the climate indicators have different impacts on Canada and the US. In the Canadian farms, the effects of higher temperature are vague while the US agriculture is more vulnerable against warmer temperature. However, the reaction to precipitation changes is similar for both countries; more (less) precipitation will increase (decrease) the farmland values. The second regression shows that the response functions to temperature are significantly different in Canada and the US.  However, before Mendelsohn and Reinsborough (2007), several Ricardian studies had been done for the Canadian agriculture. Since the spatial focus of this study is on Canada, three Ricardian applications in this country are explored as follows.  Reinsborough?s? paper (2003) was one of the first studies in which Ricardian framework was used to find how climate change affects the agricultural land value in Canada. As an extension to the model, he analysed the model based on non-uniform climate change scenarios as well as uniform scenarios. He also considered two models of farmland and farm-revenue values. The results for the uniform and non-uniform scenarios are presented in table ?2.4. In the uniform scenario, the truncated1 impact in the farm-revenue model ___ as the most preferred case ___ shows only $1.5 million annual positive change which is negligible compared to the annual gross farm revenue ($32 billion). As we can see in table ?2.4, under the non-uniform scenario, the results show even smaller change in the farm revenues, however, the direction of changes are similar to the previous scenario. Moreover, the author discussed the assumption of perfect adaptation as the shortfall of the Ricardian analysis and indicated that the costs of adaptation are considerable and long term, so it cannot be ignored. At the same year, Weber and Hauer (2003) extended the Reinsborough's analysis to provide a more detailed evaluation of climate change effects on Canadian agriculture. They used climate data for a detailed 10*10 km grid in order to concentrate on productivity variations that were caused by the local soil and climate conditions. As opposed to the Reinsborough's study, the result shows remarkable annual benefits of 5.24 billion dollars for the Canadian                                                  1. Land prices cannot be negative in calculation of a truncated impact. 22  agriculture from climate change. However, they believe that the mentioned benefit would be the maximum potential benefits, not the actual one. Table ?2.4: Predicted Changes in Farmland Value (in 1995 $CDN), Reinsborough (2003)  Uniform climate change Non-uniform climate change Weight Truncated Non-Truncated CGCMI1 GAX2 CGCMI GG13 Farmland $985,000 $897,000 $913,000 $638,000 Farm Revenue $1,483,000 $1,396,000 $769,000 $689,000 Source: Reinsborough (2003) In a recent paper (Amiraslany, 2010), the author employed the Ricardian model for the Canadian Prairies to examine the global warming effect using Census Subdivision (CSD) data for three years of 1991, 1996 and 2001. As an extension, he relaxed the assumption on the constant market price which was considered in the original model in order to obtain a more accurate result. The results of this paper are consistent with the previous studies in Canada in which farmers will benefit from climate change. The main features of this study is using panel data and also employing climate normals for a period of 20 years before each census year instead of unique climate normals for all periods. In fact, the author calculated three 20-year climate normals for each census year (1972-1991, 1977-1996 and 1982-2001), whereas other related research used a 30-year climate normals for all census years. Therefore, as opposed to the similar works, climate normals are time-varying in the Amiraslany?s study.  Some of the research that used panel data for estimating the Ricardian model are presented here. Garcia and Viladrich (2009) examined the changes in Spanish farmland acreage as well as farmland price. They used annual provincial data for the period 1983-1999 to examine the joint effects of plausible climate change on rainfed and irrigated farmland price and acreage through 2050. The long term averages (climate normals) was added as new variables to the                                                  1. Canadian Global Coupled Model 2. The effects of greenhouse gases and aerosols are included. 3. Only the effects of greenhouse gases are considered. 23  model. This study concluded that for rainfed farmlands the price goes up but the acreage goes down. On the other side, the price and acreage of irrigated farmlands increase due to the climate change. Massetti and Mendelsohn (2011) also used panel data to assess the impacts of climate change on the American agriculture. The panel data were collected from 48 states in the United States for six agricultural census years of 1978, 1982, 1992, 1997 and 2002. A key contribution of this paper is showing that if data for several years are available, estimating a Ricardian model using panel data methods would lead to stable results whereas the repeated cross section data would not. The climate variables are considered to be time-invariant since they used 1971-2000 climate normals data for all periods of time. As we can see, different approaches are adopted to deal with the Ricardian model. Using these approaches, the conceptual framework and methodology will be presented in the next chapters.    24  Chapter 3: Theoretical Framework In this chapter the conceptual framework of the study is described. We start in Section 3.1 by introducing the previous production function approach?which was the first method to examine the relationship between climate and agriculture. Section 3.2 discusses the Ricardian model, which was introduced by Mendelsohn et al. (1994) as a response to the flaws of the production function approach. The original Ricardian model utilized cross section data and thus assumed fixed commodity prices. Amiraslany (2010) utilized panel data and in doing so relaxed the fixed price assumption (details in section ?3.3). The adaptive price expectations approach, which improves upon Amiraslany?s? (2010) method of including time-varying output price in the Ricardian model, is discussed in Section 3.4. 3.1. Production Function with Climate Factors A simple traditional production function could be used to assess the economic effects of climate change on agriculture. Hill et al.?s?paper (1979) was one of the first studies in which climate factors were included in a production function as inputs in order to predict farm yields from climate data. The appropriate equation is                   i  1  ?  n ?3.1 where Qi indicates the production of good i, Ki = (Ki1,??,?Kim) is a vector of m required inputs for producing good i, and CL = (CL1, CL2, ?,?CLr) is a vector of r exogenous climate factors. Then, given the market price of good i, Pi, farmers choose K1, K2,? ?, Kn to maximize their profit across n products:   ?                     ?3.2 Within Equation  ?3.2 Ci represents the cost of producing good i and w is a vector of input prices. This simple model assigns a link between climate factors and profit via agricultural production. Specifically, adverse values of one or more of the climate variables in climate 25  vector, CL, can reduce Qi for a given set of inputs: Ki, which is equivalent to raising the cost of producing Qi units of output. Therefore, by using this model, the effects of different climate change scenarios can be evaluated.  Equation  ?3.2 can be represented graphically. First consider the case where it is not possible for the farmer to adapt because only one crop (e.g., crop 1) is grown. The left most graph in Figure ?3.1, which was adapted from Mendelsohn et al. (1994), shows the economic value of crop 1 as a function of a climate variable like temperature. Notice that after point A, a further increase in the temperature causes the value of wheat production to drop dramatically. Hence, it appears that climate change has very severe implications for the welfare of this farmer. If the farmer was able to produce n crops rather than just one crop then substitution is possible. In Figure ?3.1 the farmer will switch from crop 1 to crop 2 to reduce the cost of climate change (i.e. adapt) after temperature has risen to TA. The same analysis is applicable for points B and C. This simple example indicates why a production function approach with a single crop can result in a biased estimate of the impact of climate change. Figure ?3.1: The Process of Adaptation  Adapted from Mendelsohn et al. (1994)  Crop 1 Crop 2 Temperature of Environmental Variable Crop 3 Value of Activity A B C Crop 4 TA TC TB 26  3.2. Ricardian Model A response to the previously discussed drawback of the production function approach is the Ricardian model. This model was introduced by Mendelsohn et al. (1994) to avoid the overestimation of agricultural damages due to climate change which was inherent in the production function approach. In other words, the Ricardian model accommodates shifts in the production functions due to climate change (The heavy solid line in Figure ?3.1). Following?Mendelsohn?et? al.?s?paper? (1994),? the?Ricardian?model?will?be?described? in? this?section. The standard Ricardian model has several critical assumptions: 1. Farmers use lands in ways which maximize farm profits, 2. All inputs and outputs have perfect-functioning markets, 3. Climate change happens immediately and the economy is fully response to these changes  4. The input and output market prices are constant (Reinsborough et al. 2003) The main concept of the Ricardian approach is that there is a correlation between climate variables (e.g. temperature and precipitation) and farmland value or net rent because the crop yields and the cost of production are both dependent on the climate. Therefore, instead of modeling the crop yield as is the case in the traditional production function approach, the farmland value is the main variable of interest in the Ricardian model. This substitution allows the analyst to take into account the indirect effects (adaptations) as well as the direct effects of global warming on agriculture. In the Ricardian model the hypothesis is that the production function can be shifted while the climate factors change. In this model, the environmental situation is assumed to be given to farmers and they adopt new practises (e.g. switching to a new crop, substituting inputs and employing new technology) for adapting to climate change.  In Figure ?3.1, the vertical axis is assumed to be the output value minus the value of all inputs, except farmland rent. Farmland rent is necessarily equal to the net yield of the best use of the farmland (the solid line) given the assumption of competitive markets. If the temperature 27  happens to be less than TA, then a farmer would choose to produce crop 1 which is the most profitable crop. If, however, temperature goes up every year then crop 1 becomes less profitable and farmland value comes down to reflect the lower profitability of crop 1. The farmer will find it profitable to continue to cultivate crop 1 until the temperature reaches TA. At point A, the farmer is indifferent between producing crop 1 and crop 2. However, once the temperature goes above TA, crop 2 becomes more profitable and the farmer will switch to producing crop 2. A similar process will happen at points B and C in which the farmer will switch to crop 3 and 4, respectively. Thus, the farmland value must necessarily capture the indirect impacts of climate change (adaptations) on agriculture.  To show this relationship mathematically, consider the profit function with farmland rent cost separated from the other costs,                          , ?3.3 Within Equation 3.3 PL is the annual farmland rent and Li is the amount of land used for producing good i given CL and w. Under perfect competition, farmers choose Qi such that the price of good i becomes equal to the marginal cost                    ?3.4 The optimal output, Qi*, can be obtained by solving Equation ?3.4. Plugging Qi* into the Equation ?3.3 leads to                            .  ?3.5 A farmer compares the profits of all competing commodities and chooses the best one. Consequently it is acceptable to drop subscript i and put the notation?**?to?show?the?farmer?s?most profitable choice. To obtain the land value from Equation ?3.5, we set the profit equal to zero since competition drives PL up until the profit becomes zero. Then, PL,t, the farmland rent as of time t, is obtained from Equation ?3.5 as follows: 28                               .  ?3.6 Within Equation ?3.6 Pt is the commodity price at time t. The market rent of land, hence, is equal to the annual net profit per unit area. Following Campbell and Shiller (1987), the present value of the stream of future net revenue must equal           ?          (      )           ?           (                      )        ?3.7 Within Equation ?3.7 Et(.) denotes the expectation of a variable at time t and r showing the interest rate.  Equation ?3.7 is the main point of the Ricardian approach. According to this equation, the effect of changes in climate variables is captured by the change in the value of land. In detail, climate variables (CL) have a direct impact on farmland value by changing the cost and have an indirect impact by changing the optimal production. After a change in the climate, the farmer may choose to produce new crops and employ new technology, which in turn will impact the net revenue stream. Farmland value is therefore determined by long-term net revenue accumulation, which corresponds to the definition of farm welfare. Therefore, the welfare impact of climate change can be obtained by estimating the corresponding change in the farmland value.  Using the concepts of welfare and supply curves, Figure ?3.2 shows the farm adaptation process. . According to this diagram, before climate change (CL1) crop 1 is chosen by the farmer, since the farm welfare from producing crop 1 is larger than crop 2 (P1HE>P2AC). However, after climate change (CL2) the welfare from cultivating crop 2 becomes larger than the welfare from crop 1 (P1GF<P2BD). Hence, the farmer will switch to crop 2. As farmland value is the proxy measure for welfare, incorporating the value of farmland in the model can reflect the above adaptation process in the analysis. 29  Figure ?3.2: Welfare impact of climate change  3.3. Ricardian Model with Variable Output Prices The framework for relaxing the constant price assumption in the Ricardian model is adapted from Amiraslany (2010). The fixed market price assumption in the original Ricardian model may potentially cause two problems: 1) bias in empirical estimation which arises from excluding a significant variable (e.g. price); and 2) bias in welfare measurement.  Figure ?3.3 : Direct and Indirect Effects of Environmental Factors on Profit  Adapted from Amiraslany (2010) Crop 1 Crop 2 Q P P2 P1 A B D C E F G H CL1 CL2 CL1 CL2 ?i Pi F(?) CL 1(2(3(4( 5(6(30  Figure ?3.3 graphically illustrates how the climate factors can influence the profit directly and indirectly. As shown in this figure, the constant price assumption by the traditional Ricardian model overlooks the impacts of price on profit via lines 5 and 3, and 4 and 1. Indeed, F(?)? is? a? function? of? other? influential? variables? like? policy,? technology, and production which can be affected by price as well. As was mentioned earlier, if price changes are ignored bias in the measurement of welfare (farmland value) is the other potential problem of the Ricardian model. To illustrate this issue,? let?s? start?with? a? scenario? in which the supply curve shifts to the left due toclimate change, such as a drop in temperature.  Assuming the price is fixed as it is in the Ricardian model, Figure ?3.4 shows that the supply reduction from climate change shifts the new equilibrium from A to D. Consequently, the new level of welfare for the farmer is P0DE. However, if the price increases during this process, the welfare will actually be P1CE which is larger than the first case. As a result, the fixed market price assumption causes an overstatement of the welfare loss due to a climate change impact. In other likely scenarios, like a supply increase or a price decline (the dashed lines in figure ?3.3), holding the price constant may understate the welfare loss. Misestimating the welfare, due to ignoring the commodity prices, will typically affect the measurement of the adaptation process. Figure ?3.4: Supply Reduction Effects  Price Quantity S0 SE A B C E P1 P0 D 31    Figure ?3.5: The Impact of Price in Adaptation Process  In figure ?3.5, the market price is added to figure ?3.2 to evaluate its impact on the adaptation. We saw in figure ?3.2 that the farmer would switch from crop 1 to crop 2 if the climate factors change from CL1 to CL2. Now, assume that the prices change due to a climate change as well (Figure ?3.5). According to the figure, the price of both crop 1 and crop 2 will surge. However, notice that the increase in the price of crop 1 is much larger than that of crop 2 (P1?- P1> P2?- P2). Hence, since the welfare from producing this crop is still larger (P1?KF> P2?JD),?the farmer continues to produce crop 1 after climate change. If we ignore the change in the commodity prices in our analysis, the farmer should cultivate crop 2. Therefore, the fixed price assumption in the original Ricardian approach seems to cause a bias in the analysis and it is necessary to improve it by incorporating the price change into the model. 3.4. Adaptive Expectations In?Amiraslany?s?study?(2010),?it?is?assumed?that?the?farmers?look at the market output price in each census year and then determine the farmland value based on that information. This assumption implies that farmers believe that the best forecast of all future prices is the Crop 1 Crop 2 Q P P2 P1 A B D C E F G H CL1 CL2 CL1 CL2 P?1 P?2 I J K L 32  current price. If the current price, P0, is substituted for the expected price in Equation 3.7 then the resulting equation can be written as            ?         (                 )      ?3.8 This equation simplifies to ? ? rwCLQCQPVt /),,( ****0** ?? . This formulation demonstrates that comparatively small changes in the current price of the commodity will have large impacts on the price of land. In reality the price of land is much less volatile than that implied by Equation 3.8. The price of land is relatively stable because the expected price changes slowly in response to a change in the actual price. This scenario is well illustrated in Figure 3.6 for a hypothetical data. In general, using incorrect beliefs about how a price will evolve over time will certainly bias the econometric results concerning the relationship between climate change and the price of land. Figure ?3.6: Compare Expected Price to Current Price of a Hypothetical Commodity   To obtain the price expectations, Et(Pt+i)?in?the?former?equation,?we?employ?the??Adaptive Expectations Hypothesis? which was introduced by Cagan (1956) and Nerlove (1957). This hypothesis states that the expected value of an economic variable, Et(P), is formed adaptively according to the following equation,  33                     (           )  ?3.9 Within Equation 3.9 note that 0<b<1 is the coefficient of expectations. By solving Equation ?3.9 for          and then applying repeated substitutions, the equation becomes               1             ?3.10                          1           1              Note that this model assumes that all future commodity prices are the same as the next period. Then, Equation ?3.10 can be written as                 1           1             ?3.11 The above equation is an expression for the expected price in Equation ?3.8. It shows that expected price can be expressed as a weighted average of the past values of the economic variables with geometrically decreasing weights. The coefficient of expectations, b, demonstrates how quickly the farmland value responds to changes in the actual commodity price. By plugging Equation ?3.11 into Equation ?3.8, we can observe that the farmland value not only depends on current commodity prices but also on all past prices. Thus, in addition to the standard set of explanatory variables which are included in the Ricardian model, it appears appropriate to also include the lagged prices into the regression equation:                              ?3.12 Within Equation 3.12 X is the matrix of control variables other than? prices? and? ?? is? the?coefficients vector. Theoretically, n should go to infinity; however, we consider a finite number of lagged prices in the present study in order to make the estimation possible. The procedure for selecting the optimal number of lags will be described below. 34  Chapter 4: Methodology Chapter 4 begins with introducing and explaining the dependent and independent variables of the model. Then, the empirical methods which are used to estimate the model will be described. Several regression approaches can be utilized for the panel data analysis. The first approach is pooled least squared regression which is similar to cross sectional regression. For the second approach, the fixed effects and random effects models ___the two popular methods for panel data analysis ___ will be examined to identify the more appropriate method. At the end of this chapter, we clarify how to deal with the problematic issues in the regression analysis and also how to use the estimated model to predict how climate change is expected to impact farmland values.  4.1. Variables Dependent and independent variables in this study are consistent with other studies which utilized the Ricardian model. Independent variables can be categorized into climatic and non-climatic variables. The climatic variables include selected climate normals and characteristics. Theon-climatic variables consist of current and lagged market prices: variousregional control variables, and an assortment of regional dummies.  Census Subdivision (CSD) data for five census years (1991, 1996, 2001, 2006, and 2011) is used to estimate the model. CSD is the smallest available unit for spatial analysis since it is the lowest level of Statistics Canada Standard Geographical Classification (SGC). In the following section, all variables will be introduced and interpreted. 4.1.1. Dependent Variable As was mentioned in the previous chapters, the farmland value (per unit area) serves as the dependent variable in Ricardian models. In the present study, the total land and buildings market value ($CDN) are extracted from the Canada Census of Agriculture for five census years. By dividing those values (in constant 2002 CAD) in each CSD by its area (hectare), the data for average farmland value is specified in terms of $CDN/hectare. This variable is defined in its logarithm form.  35  4.1.2. Independent Variables: Climate Variables Temperature, precipitation, and humidity are the three main climate characteristics which are included in the model. The climate data are extracted from the 1971-2000 climate normals which were published by Environment Canada. In fact, since climate change is a long term shift in the weather condition, we consider the climate variables fixed over the 5 census periods. As suggested by the literature, the climate variables which are used in the model are as follows.  - Temperature: Climate-normal average temperatures are taken for the months of January, April, July and September. Since the temperature impact on farmland value varies across seasons, the temperatures of these months are included in the model and are assumed to be representative of each season.  - Frost Free Days: The monthly mean number of days with positive temperature. - Precipitation: Climate-normal average rainfall and snowfall for the months of January, April, July, and September. - Evapotranspiration: This variable, which reflects the main part of water cycle, is the sum of evaporation and transpiration. Evaporation accounts for the water movement from the sources like soil and water bodies to the air; transpiration accounts for the water movement from plants to the air. Evapotranspiration is calculated by dividing the climate-normal annual average precipitation by climate-normal annual average temperature.  As the climate data are available for weather stations, we need a mechanism to calculate the climate properties of each Census Subdivision. For this purpose, only those stations which are situated less than 100km from the centre of each CSD are considered. Then, the weighted average of climate data is calculated based on the proximity of stations to each CSD.  36  Table ?4.1. Variables   Variable Symbol Source Dependent  Market Value of Land and Building FLVAL Census of Agriculture Independent Climate Variables Temperature JANT, APRT, JULT, SEPT Environment Canada Rainfall RAIN Environment Canada Snowfall SNOW Environment Canada Evapotranspiration EVAP Environment Canada, Author Frost Free Days FFD Environment Canada Dummies Soil Zone BLACK, BROWN, DBROWN, GRAY, DGRAY C-RERL (The Canada Rural Economy Research Lab) Time 1991, 1996, 2001, 2006, 2011 Author Price Grains price PG0, PG1, PG2,?? Statistics Canada, Census of Agriculture Cattle price PC0, PC1, PC2,?? Statistics Canada, Census of Agriculture Control Variables Per Capita Income INC Census of Population Population Density POP Census of Population Government Transfers GOV Census of Population Longitude longitude Census of Population Elevation elevation Census of Population Distant to Closest Highway HWAY C-RERL  Distant to Closest Export Terminal EXP Google Map, Author 37  Table ?4.2: Summary of Variables Variable Obs Mean Std. Dev. Min Max Farmland Value (CAD/ha) 1690 1349.80 1012.57 276.95 11659.38 January Temperature (?C) 1690 -16.60 2.21 -19.88 -7.64 April Temperature (?C) 1690 3.73 0.77 1.96 6.02 July Temperature (?C) 1690 17.83 0.99 13.91 19.50 September Temperature (?C) 1690 11.06 0.78 8.74 12.62 Rainfall (mm/year) 1690 332.81 47.68 241.33 435.49 Snowfall (cm/year) 1690 107.03 16.31 70.32 210.01 Evapotranspiration (mm/?C) 1690 314.44 307.15 -314.97 1867.87 Frost Free Days 1690 159.88 7.20 134.61 181.33 Grain Price index 1690 78.33 14.66 58.57 108.30 1-Year Grain Lagged Price Index 1690 80.05 13.74 55.19 100.87 2-Year Grain Lagged Price Index 1690 89.23 16.70 68.18 118.76 3-Year Grain Lagged Price Index 1690 83.75 8.18 66.17 101.99 4-Year Grain Lagged Price Index 1690 76.45 10.60 58.33 95.55 5-Year Grain Lagged Price Index 1690 79.69 15.08 56.01 108.46 Cattle Price Index (Weighted) 1690 2336.45 4640.61 12.18 75954.50 1-Year Cattle Lagged Price Index 1690 2375.30 4715.23 10.46 73277.80 2-Year Cattle Lagged Price Index 1690 2380.83 4726.28 10.18 69282.53 3-Year Cattle Lagged Price Index 1690 2468.34 4851.85 10.30 66534.04 4-Year Cattle Lagged Price Index 1690 2542.38 4961.64 10.66 64872.64 5-Year Cattle Lagged Price Index 1690 2552.36 4981.73 11.21 68554.30 Per Capita Income (?1000) 1690 13.00 4.23 4.33 47.55 Population Density (?1000/km) 1690 0.03 0.11 0.00 1.08 Government Transfers (?1000/ha) 1690 0.03 0.06 0.00 1.39 Longitude 1690 -104.78 4.64 -117.14 -95.99 Elevation (m) 1690 567.53 171.15 241.71 1344.49 Distant to Closest Highway (km) 1690 43.72 39.30 0.00 197.00 Distant to Closest Export Terminal (km) 1690 1226.49 241.37 633.00 1641.00   38  4.1.3. Independent Variable: Dummy Variables Dummy variables in the model include those for soil zones for each CSD. Black, Gray, Dark Gray, Brown, and Dark Brown are the five soil zones in the Canadian Prairies which are represented by dummies.  4.1.4. Independent Variables: Control Variables Control variables contain the economic and characteristics of each CSD which have a significant role in determining the value of farmland.. The higher demand in denser, wealthier and growing CSDs is generally associated with a high farmland value. Population density (population per square km), per capita income (in constant 2002 CAD), government transfers (in constant 2002 CAD), longitude, elevation and distant to the closest highway and export terminal of the Prairies CSDs are therefore considered to be control variables. 4.1.5. Independent Variables: Market Price Variables Price variables are included in the Ricardian model to project the impacts of market on farmland values. The price of grains (wheat, barley, canola and alfalfa) and cattle are chosen to be included since these commodities represent the largest share of farms, cash receipts and cultivated area in the Canadian Prairies.  The farm product price index, which is compiled by Statistics Canada, is as a proxy for market prices. However, to accommodate adaptive price expectations,, lagged prices are defined as explanatory variables as well as the current price.  Moreover, as the content of grains and cattle products is different in each Census Subdivision, the weighted price index is employed. For grains, the weighting is based on the planted share of each grain. Specifically, the grains index price can be expressed as          ?         ?        ?4.1 where Pi and Ai are price and cultivated area of grain i, respectively. This price is calculated for each Census Subdivision. To obtain the weighted cattle price index in each Census Subdivision, the number of cattle is multiplied by the cattle price index. Specifically, 39                     ?4.2 where N is the number of cattle in each Census Subdivision. The list and the summary of variables are shown in Table ?4.1 and Table ?4.2. All prices are expressed in constant 2002 CAD. 4.2. Empirical Methods  In this section, the econometric framework which is used to evaluate the impact of climate properties on the Canadian Prairies agriculture is described. An econometric model should be defined such that farmland value can be regressed on climatic, dummies, and control variables ___ which were introduced in the previous section.  Various econometric strategies have been used in the past to estimate the Ricardian model including: the cross sectional model, the pooled panel model, and the fixed effects model. In this section, these empirical approaches are explained along with the random effects and the spatial random effects models, which are employed in this study. 4.2.1. Cross Section Approach The cross sectional approach is the basic method that has been used to estimate the Ricardian model. In the majority of traditional Ricardian model studies, the long term impacts of climate change on agriculture were evaluated using the cross sectional analysis since only one year of data was available to estimate the model. This approach was based on the following equation                      , ?4.3 where V is the logarithm of farmland value per unit area, X is a vector of control variables, Z shows a vector of dummies (i.e. soil zone and year), C is avector of climate variables and u is the error term. The subscript of i varies across regions. After Equation  ?4.3 has been estimated, the model can be used to assess the impact of climate change by estimating the change in farmland values due to a potential change in the climate variables. 40  To increase the robustness of cross sectional methods, the first idea was using multiple years of data as the repeated independent cross section. For this case, Equation 4.1 changes to                                        1              1         ?4.4  where ui,t is an idiosyncratic error term which changes over time and across CSDs. The variables with a t subscript vary over time. This method is used by Deschenes and Greenstone (2007) to estimate the climate change effects on U.S. agriculture. However, Massetti and Mendelsohn (2011) argued that the repeated cross section approach is mis-specified, since the coefficients of time varying variables (?)?should?be?fixed?over time. They employed both a?single?stage??pooled??model and a two-stage model and then showed that if panel data is available, the panel methods yield stable results while the repeated independent cross section method does not. As the data for the climatic and non-climatic variables are available for several census years, the panel data approach seems to be the most fitted econometrics method for the current study. 4.2.2. Panel Data Analysis One of the most crucial problems in statistical models is how to control for unobservable variables.? Experimental? researchers? solved? this? issue? by? applying? ?random? selection?? in?collecting data process. However, this problem seemed to be more complicated for non-experimental studies. Introducing panel data analysis was an effort to deal with the mentioned issue in non-experimental research (Allison, 2005).  A panel data set contains multiple observations for each individual over a number of periods. This data set has several advantages over other data sets like cross-sectional and time-series. Panel data improves the efficiency of econometrics estimates by: providing a numerous data points; decreasing the collinearity among the independent variables; and increasing the degrees of freedom (Hsiao, 2003). 41  In the present study ___ using panel data analysis ___ the pooled, random effects and spatial panel models are utilized to regress farmland value on the climatic and non-climatic explanatory variables. The details about all the three methods are provided below. 4.2.2.1. The Pooled Regression The simplest way to estimate a panel data model is to pool the entire observations of the five census years and estimate the model using a least squared method. We consider the following regression model                                         ?4.5  where Pit shows the current and lagged prices of grains and cattle, ?t indicates the time period dummies, and the other variables are described in the previous sections. The above model, in fact, is not a fully pooled model as it contains dummies for each time period. The double-subscripted notation (i, t) indicates that we are working with a panel data set. The impacts of climate variables and the other control variables will be obtained by the estimation of Equation ?4.5 coefficients (?, ?, ?, ?, ?, and ?) using the least squared method.  The quadratic form of climate variables (i.e. Ci2) in Equation ?4.5 captures the possibilities of nonlinearity for these variables which is consistent with the literature. The linear term of climate variables shows the marginal value of climate and the quadratic term represents the shape of relationship between the farmland value and climate properties. The sign of the coefficient of the quadratic term determines whether the relationship is hill or U-shaped. A negative sign shows that the relationship ___ between the climate variables and farmland value ___ is hill-shaped and U-shaped otherwise. (Mendelsohn, 2001) Although the pooled regression model can control for the time effects by incorporating time period dummies, it implicitly assumes that all the coefficients (including the intercept) are the same for all the regions. As a result, this model neglects heterogeneity across regions. If each region has a unique effect on farmland values, those effects are subsumed in the error term. In this case, if the explanatory variables are correlated with the error term, the estimates will be inconsistent and biased.  42  The similar issue would arise if each year has a unique impact on the dependent variable as well. The fixed and random effects models are the most commonly used estimation models which capture the unobservable region and time effects. .  4.2.2.2. The Fixed and Random Effects Models The basic idea of fixed and random effects methods is using each individual- level as its own control. A basic panel model is defined as below                                    ?4.6 where              , ?4.7  Within Equation 4.7 ?t and? ?i reflect unobservable temporal and regional effects, respectively,?and??it shows the remainder disturbance. The subscripts i and t changes across CSDs and the five census years (1991, 1996, 2001, 2006 and 2011).  In the fixed effects model, the unobservable time and region effects (?t and??i) are assumed to be the fixed parameters whereas in a random effects model, they are random. Moreover, the explanatory variables are assumed to be correlated with ?t and??i in a fixed effects model and uncorrelated in a random effects model. Estimation of a fixed effects model can be accomplished with OLS and using the mean deviation algorithm. The first step of this algorithm is calculating the means of each time-varying variables (dependent and explanatory variables) over time for each CSD  ?    ?                      ?    ?      , ?4.8 where N is the number of available data for each CSD. Then, the two new variables are defined by substracting the mean of each variable from the observed values for each CSD: 43            ?                            ? , ?4.9 The final step is regressing Yit* against Xit* and time effect variable. Since the time-invariant variables disappear during the demeaning process, the fixed effect model is not capable of estimating the coefficients of these type of variables (Allison, 2005). Random effects model can be estimated using Generalized Least Squares (GLS) which lets us estimate the time-invariant variable. Following Allison (2009), based on the specifications of the fixed and random effects model, we should choose one which is more appropriate for the current study. Two main criteria could affect the choice between these two models:  1. The nature of omitted variables: If there is no omitted variable or the omitted variables and explanatory variables are uncorrelated, then the random effects model would be the best. It will give us unbiased estimates and the smallest standard error. Conversely, if we think there are some omitted variables which are correlated with explanatory variables, the fixed effects model should be chosen.  2. The type of variables of interest: As mentioned before, although a fixed effects model could control for time-invariant variables, it is unable to estimate their coefficients, whereas a random effects model will estimate them.  The second criteria demonstrates that the fixed effects model is not an appropriate approach since the climate variables are time-invariant and estimation of their coefficients is the main purpose of the current work. For evaluating the first criteria, we show that the climate variables, as the main variables, are not correlated with the error terms. For this purpose, after estimating the model, the correlation coefficients between the error terms and climate variables, and their significance are obtained. The results1 indicate that the error terms and the climate variables are not correlated. Therefore, the random effects model will be utilized as a second method (the first one was the pooled regression) to estimate the coefficients of the Ricardian model.                                                   1. The correlation coefficients are shown in section ?5.1.1. 44  4.2.2.3. Spatial Panel Model Failing to acount for spatial characteristics in a Ricardian model may cause spatial autocorrelation and as a result biased and inefficient estimators (Kaltsas et al., 2000). In the spatial approach, we deal with spatial interaction (spatial autocorrelation) in the regression model to consider how farmland value at a given CSD would be affected by farmland values at other CSDs in the Canadian Prairies. In other words, spatial autocorrelation approach lets us include the degree of dependency of farmland value amongst CSDs into the Ricardian model. To capture the spatial autocorrelation in the Ricardian model, an independent variable can be incorporated to the model as a spatial lag of the farmland value. Following Anselin (2001), we define a spatial autocorrelation model (SAR) as below                                                 1              1        ?4.10 where W denotes the spatial weights matrix? and? ?? is? the? spatial? autoregressive parameter. The N?N spatial weights matrix (W)? specifies?which?CSDs? affect?which? others?? farmland?values. In fact, the ith row of matrix W demonstrated how much farmland value at the CSD i would be affected by the other CSDs.  Note that WVi is called a spatial lag for V at i which is the weighted average of farmland value at neighboring CSDs:       ?              ?4.11  where wij is ijth entry of matrix W. The elements of the spatial weights matrix (wij) are exogenous and nonstochastic which are obtained based on the geogeraphic arrangement of CSD. In this study, matrix W is generated using the Canadian census subdivisions shapefiles 45  which have been published by Statistics Canada.1 We utilize spatial contiguity weights in which the matrix indicates whether or not CSDs share a boundary. Therefore, the elements of matrix W (wij) would be zero if there is no common boundary between the CSDs i and j, and one otherwise.  Maximum likelihood estimation (MLE) is used as the econometrics method to estimate the coefficients of Equation ?4.10. ML estimation of the SAR model is done by maximizing the log likelihood function with respect to the spatial? autoregressive? parameter? (?).? The log likelihood function for the SAR model is (Anselin, 1988):         |     |  (  )                                                          ?4.12 where X is all the explanatory variables and n is the number of CSDs. The above procedure is done using the Stata module for spatial panel data models estimation2 by Belotti et al. (2013).  4.2.3. Potential Problems in Regression Analysis  By running the regression using each of the above methods, one will be able to determine the contribution of each explanatory variable to the farmland value. However, there are some possible issues which violate the assumptions of the regression models. Heteroskedasticity and multicolinearity are two of these potential problems that are discussed in this section. Heteroskedasticity violates one of the basic assumptions of the regression model: the error is distributed with constant variance. This issue may arise where the values of at least one variable have a large range; the growth rate of the dependent variable over time is                                                  1. By using spmat command in Stata. 2. The Stata command is xsmle which is a new command for estimating and forecasting spatial panel data models. 46  significantly different from the one of independent variables; and the data are not homogenous (Wang and Jane, 2003). Although heteroskedasticity does not cause a biased estimation, it leads to inefficient estimates by underestimating the variance of coefficients. In forcast modeling, estimations need to be both unbiased and effiecient. (Wang and Jane, 2003)  Looking at the structure of data, all three causes are plausible in this study, thus, considering this problem seems necessary. To detect heteroskedasticity in the current model, White?s? general? test is used 1 . In this test the null hypothesis is constant variance (homoskedasticity) which is rejected at significant level of 0.01, thus, heteroskedasticity occurs in our data. As heteroskedasticity leads to biased standard errors, relaxing the assumption of independent and identically distributed error can give us more efficient estimates. To deal with this issue, robust standard errors (also referred to Huber/White estimators) will be used in the estimations to relax the above-mentioned assumptions. Moreover, Weighted least squared (WLS) can control for heteroskedasticity by giving more weight to the observations with smaller variances (Greene, 2003), thus, we employ WLS instead of OLS for the pooled estimation.  Multicollinearity occurs where one of predictors in the model is a linear combination of at least one of other predictors. In this case, two or more independent variables are correlated and have redundant information on dependent variable. Multicollinearity may cause high standard errors of estimates, large marginal effects and also shows a large R2 while there is no significant predictor (Mendenhall and Sincich, 1996).  There is a concern about existing multicollinearity in the current model since the climate variables and their squared terms are obviously correlated. Bradley & Srivastava (1979) show that mean-centering of the independent variables in a polynomial regression can reduce the correlation between the linear and powered terms. Therefore, for this study all the climate data will be subtracted from their average before generating the squared terms.                                                  1. Done by whitetst command in Stata 47  4.3. Prediction  After estimating the coefficients of the Ricardian model, one can apply different climate scenarios to the model for predicting the impacts of future climate changes on the farmland value. In order to simulate the change in farmland value due to the climate change, recall the estimated model   ?    ?   ?   ?  ?    ?     ?     ?     ?     ?4.13 where  ?   is the fitted farmland value. The new potential values for the climate variables (C') should be plugged into Equation ?4.13  ?     ?   ?   ?   ?     ?      ?     ?     ?     ?4.14 The change in farmland value can be predicted by substracting Equation ?4.13 from ?4.14:     ?          ?(        )    ?4.15 Moreover, the impact of changes in grain and cattle prices can be considered in the model as well by including price change scenarios in the model. Then, the change in farmland value would be     ?          ?(        )   ?          ?4.16 By plugging new climate and price values (which are calculated based on different scenarios) and the current values into Equation ?4.15, changes in the farmland value can be calculated for each CSD. The t subscript is dropped from the prediction equations since we use the climate and price data of the most recent time period (2011) to forecast farmland values.  48  Chapter 5: Empirical Analysis  In this chapter, the impact of climate normals on the economy of agriculture in the Canadian Prairies are assessed based on the three econometrics approaches introduced in the previous chapter ___ the pooled, random effects, and spatial panel data estimations. Then, the estimated coefficients of the Ricardian model using each method will be compared and the results will be discussed. 5.1. Estimation Results In this section, the coefficients of the Ricardian model are estimated using the three different approaches. In the first approach, the model is estimated by the pooled weighted least square model (WLS). We choose WLS instead of OLS to control for heteroscedasticity and use farmland area by census subdivisions in each census year for a weight.  In Chapter 3, we showed that farmland value depends on the previous prices (via adaptive price expectations) as well as the current price. The inclusion of the current and lagged prices enables the model to capture the effect of market on farmland price; moreover, the estimation of current price impact can be used to predict the effect of price fluctuation on farmland value. By incorporating the limited lagged prices to the model we actually construct a finite distributed lags model. In a finite distributed lag model, a dependent variable is regressed on both the current and finite past values of explanatory variables (Judge et al., 1985). To show the necessity of incorporating lagged prices in the model, the WLS estimates for two models (with and without the lagged prices) are presented in Table ?5.1. To determine the number of lagged prices in the model, we run 9 separate regressions. In the first regression, we incorporated only one lagged price and in the second one, two lagged prices were included in the model and so on. After running the 6th regression, many of lagged prices were omitted due to collinearity. Hence, we chose to consider five lagged prices in our Ricardian model. Comparing the estimated parameters in the first and the second columns of Table ?5.1, we can see that the coefficients of current and lagged prices are all significant.  49  Table ?5.1: Weighted Least Square Estimation Results  Variable Pooled WLS (No Lagged Price) Ra2 = .777 Pooled WLS Ra2 = 0.796 Climate Variables January Temperature  -0.0434*** -0.028* January Temperature - Squared 0.0189*** 0.017*** April Temperature  0.1830*** 0.193*** April Temperature - Squared -0.028 -0.018 July Temperature  0-.1981*** -0.133* July Temperature - Squared 0.005 0.025 September Temperature  0.1747** 0.125* September Temperature - Squared -0.0722** -0.087** Rainfall  0.0086*** 0.008*** Rainfall squared 0.000052*** 5.66E-05*** Snowfall -0.0053*** -0.004*** Snowfall squared -0.00002307 -2.37E-05 Evapotranspiration -0.00017*** -1.40E-04*** Evapotranspiration squared 9.857e-08* 6.19E-08 Frost Free Days -0.0092** -0.011*** Frost Free Days squared 0.0009*** 0.001*** Dummies Black Soil Zone 0.261*** 0.203*** Brown Soil Zone 0.082 0.037 Dark Brown Soil Zone 0.2062*** 0.155*** Gray Soil Zone - - Dark Gray Soil Zone 0.203*** 0.181*** 1991 0.149 - 1996 - -0.949* 2001 0.167 -0.011 2006 0.320* 0.674** 2011 0.5142*** -1.205*** Price Grain Price 0.0063 0.091*** 1-Year Grain Lagged Price  -0.085*** 2-Year Grain Lagged Price  0.04*** 3-Year Grain Lagged Price  0.029*** 4-Year Grain Lagged Price  -0.056*** 5-Year Grain Lagged Price  0.009* Cattle Price 4.77E-06 0.001*** 1-Year Cattle Lagged Price  -0.001** 2-Year Cattle Lagged Price  2.30E-04** 3-Year Cattle Lagged Price  - 4-Year Cattle Lagged Price  -1.03E-04 5-Year Cattle Lagged Price  1.35E-04*** Control Variables Per Capita Income 0.02790416*** 0.026*** Population Density 0.13916771* 0.165** Government Transfers 0.96211793*** 1.044*** Longitude -0.0121989* -0.01 Elevation -0.00005 -1.10E-04 Distant to Closest Highway -0.0013*** -0.001*** Distant to Closest Export Terminal 0.0007*** 0.001***  Constant 3.456*** 2.019* * p<0.05; ** p<0.01; *** p<0.001 50  Table ?5.2: WLS, Random effects and Spatial Random effects estimation results  Variable Pooled WLS Ra2 = 0.79 Random Effects R2 = 0.83  Spatial Random Effects R2 = 0.81 Climate Variables January Temperature (?C) -0.028* 0.072* 0.116*** January Temperature - Sq 0.017*** 0.009** 0.009* April Temperature (?C) 0.193*** 0.051 0.037 April Temperature - Squared -0.018 0.033 0.055 July Temperature (?C) -0.133* -0.648*** -0.497*** July Temperature - Squared 0.025 0.019 0.060* September Temperature (?C) 0.125* 0.653*** 0.516*** September Temperature - Sq -0.087** 0.035 0.048 Rainfall (mm/year) 0.008*** 0.006*** 0.005*** Rainfall squared 5.66E-05*** 2.07E-05* 3.25E-05** Snowfall (cm/year) -0.004*** -0.002 -0.001 Snowfall squared -2.37E-05 -2.00E-05 -2.00E-05 Evapotranspiration -1.40E-04*** -3.10E-04*** -2.00E-04 Evapotranspiration squared 6.19E-08 1.66E-07 3.46E-08 Frost Free Days -0.011*** -0.011* -0.008 Frost Free Days squared 0.001*** -2.00E-04 -0.001* Dummy Control Variables Black Soil Zone 0.203*** 0.324*** -0.011 Brown Soil Zone 0.037 -0.015 -0.443** Dark Brown Soil Zone 0.155*** 0.218** -0.145 Gray Soil Zone - - -0.280** Dark Gray Soil Zone 0.181*** 0.280*** - 1991 - - -0.441*** 1996 -0.949* -0.008 -0.347*** 2001 -0.011 0.223 -0.176 2006 0.674** 0.318** -0.133 2011 -1.205*** 0.302* - Price Grain Price 0.091*** 0.005 -0.003 1-Year Grain Lagged Price -0.085*** -0.005 0.003 2-Year Grain Lagged Price 0.04*** 0.001 -0.003 3-Year Grain Lagged Price 0.029*** 0.004 0.002 4-Year Grain Lagged Price -0.056*** -0.016*** -0.014*** 5-Year Grain Lagged Price 0.009* 0.002 0.002 Cattle Price 0.001*** 4.30E-05 7.20E-05 1-Year Cattle Lagged Price -0.001** 4.20E-05 2.34E-04** 2-Year Cattle Lagged Price 2.30E-04** -3.00E-05 -0.001*** 3-Year Cattle Lagged Price - - 0.001*** 4-Year Cattle Lagged Price -1.03E-04 -1.77E-04*** -3.15E-04*** 5-Year Cattle Lagged Price 1.35E-04*** 1.31E-04*** - Other Control Variables Per Capita Income (?1000) 0.026*** 0.015*** 0.014*** Population Density (/km2) 0.165** 0.010 0.003 Government Transfers (C$/ha) 1.044*** 1.055*** 1.063*** Longitude (cm) -0.01 0.009 0.009 Elevation -1.10E-04 -0.001*** -0.002*** Distant to Closest Highway (km) -0.001*** -0.002*** -0.002*** Distant to Closest Export Terminal (km) 0.001*** 0.001*** 0.001***  Constant 2.019* 7.668*** -  Spatial Lag  - - 0.073*** 51  In Table ?5.2, the estimation results from random effects models are presented. In order to compare, the results of WLS approach (Model 1) is repeated in the first column of this table.  In the second column we estimate the parameters of our Ricardian model by a regular weighted Random effects (Model 2) and in the third column the spatial effects (Model 3) are considered in the estimation. Farmland area in each CSD is used as a weight for both models. The results of the two random effects approaches in Table ?5.2 show no considerable difference in the significance of the estimated parameters. Although R-squared in the regular random effects model is larger, the Spatial approach leads to more significant results for the estimations of coefficients of January and July temperatures. The sign of the climate parameters are the same in both random effects approaches, but some of them are of a different sign from the parameters for the WLS.  5.1.1. Climate Variables According to Table ?5.2, most of the climate variables have significant impacts on the Prairies farmland value in the WLS method. However, in the random effects models the estimates are not as significant as the WLS. To specify the marginal impact of the climate change on farmland value, recall Equation ?4.5. The marginal impact is obtained by taking partial derivative from the farmland value with respect to the climate factors,             ?5.1 Then, by taking the mean from the above equation we can obtain the average marginal impact of climate (MIC) for each climate variable                 . ?5.2  Since we use mean-centered climate variables to reduce collinearity in the model, the mean of climate data are zero. Thus, the marginal impacts of climate variables are equal to the coefficients of linear term (  . Table ?5.3 presents the marginal impact of climate variables. 52  As the model is log-linear, the marginal impacts show the percentage change of farmland value for 1?C or 1 mm/year change in climate factors.  Table ?5.3: Marginal impact of climate variables (MIC)  Pooled WLS  (Model 1) Random Effects (Model 2) Spatial Random Effects  (Model 3) January Temperature (?C) -2.8% 7.2% 11.5% April Temperature (?C) 19.3% 5% 3.7% July Temperature (?C) -13.3% -64.7% -49.7% September Temperature (?C) 12.5% 65.3% 51.6% Rainfall (mm/year) 0.8% 0.5% 0.4% Snowfall (cm/year) -0.4% -0.2% -0.05% Evapotranspiration -0.01% -0.03% -0.02% *** 1% significant level, **5% significant level The results show that a marginal increase in the January (expect in model 1), April, and September temperatures will increase the farmland value, whereas a change in the July temperature has an opposite effect. The September temperature is the most effective factor (12.5% - 65.3%) among all the variables and the January temperature is the least effective one (-2.8% - 11.5%). These results sound reasonable as September is the harvesting period for the majority of grains while there is no crop in January. Besides, as September is the last month of growing season, a warmer temperature means a longer growing season and larger productivity. A warmer July leads to more evaporation and as a result water scarcity, which can justify the negative sign of MIC for July temperature (McGinn, 2010).  Moreover, Table ?5.3 indicates that a higher annual rainfall increases the farmland value and a higher annual snowfall will decrease it. The results show that 1 unit increase in the annual rainfall and snowfall will increase and decrease the farmland value by less than one percent, respectively. The positive signs for rainfall along with the negative sign for the July temperature confirm the high dependency of the Prairies agriculture on water-related variables. 53  As is discussed in section ?4.2.2.2, to show whether or not random effects is a proper approach to estimate the current model, we should show that the correlations between error terms and climate variables are not strong and significant. These correlations and their significant levels are presented in Table ?5.4. The results demonstrate that the correlations are neither strong nor significant.  Table ?5.4: The Correlations between Error Terms and Climate Variables January  Temperature April  Temperature July  Temperature September Temperature Rainfall Snowfall  Evapo FFD 0.024 (-0.315)* 0.041 (-0.091) 0.026 (-0.272) 0.026 (-0.273) -0.032 (-0.184) -0.036 (-0.137) -0.014 (0.542) 0.019 (0.42) *Numbers in parentheses indicate significant levels 5.1.2. Grain and Cattle Prices Table ?5.2 indicates that the price and the lagged price variables are significant in model 1, but their significance is not considerable in model 2 and 3. The estimated parameters show that by one unit increase in the grain price index, the farmland value will increase by 9% in model 1, 0.48% in model 2, and it will decrease by 0.3% in model 3. Since we have used the number of cattle in each CSD as a weight, to obtain the marginal impact of cattle price on farmland value, the coefficient must be adjusted based on the cattle numbers. The results for the three models show an increase in the farmland value (/ha) by 1.1%, 0.09% and 0.15% per one unit increase in the cattle price index. These results can confirm that the agricultural commodity prices are an important component in determining the farmland price. 5.1.3. Control Variables Control variables capture non-climatic factors which influence the farmland value. Therefore, adding control variables to the Ricardian model leads to more accurate estimations. The adjusted R-squared for the model without control variable would be 0.536 which indicate that this model is not effective in prediction of farmland value, compared to the models with control variables. Therefore, it is important to have relevant variables in the model. The control variables which are considered in this study are consistent with other Ricardian models in the literature. 54  The estimated parameters in Table ?5.2 demonstrate that per capita income is positive and highly significant in all models which mean higher income causes a more expensive farmland. In fact, having wealthy residents leads to more demand for lands and as a result will push up land prices that is consistent with the economic theories. Population density has also a positive relationship with the farmland value as larger population increases the demand for farmlands. The government transfers are the other positive and significant variable in our model. In fact, one of the purposes of the government payments is reducing the financial risk for farmers against unpredictable and undesirable environmental and economic conditions. Clearly, with a lower risk more people tend to have a farmland and again the market will face larger demand and then the price will surge.  The coefficients of elevation and longitude variables have different signs in the models. The coefficient of elevation is significant and negative in model 2 and 3 which is consistent with the literature. Based on the Canadian studies, higher longitude has a positive impact on farmland since the price goes up from Manitoba to Alberta, therefore, the estimation of random effects models are reasonable in this case. The last two control variables in Table ?5.2 are the distance to the closest highway and export terminal. Being close to a highway is a considerable advantage for a farmland since the owner has easy access to big cities and markets. So, the negative and significant association of this factor with land price is logical. The distance to the closest export terminal was expected to have a negative relationship with farmland value since being close to an export terminal means low transportation cost. However, the sign of the estimated coefficient does not follow the expectations. It can show the presence of omitted variable bias. In other words, the distance to port is related to an omitted variable that is positively related to the farmland value. The air quality might be the omitted variable that has a positive relationship with farmland value and also relates to the distance to export terminal since export terminals are close to big cities (e.g. Calgary and Winnipeg) which are relatively polluted.  55  5.1.4. Dummy Control Variables The soil type can capture the productivity difference among census subdivisions. Most of soil dummies are significant in the models. The black, dark brown and dark gray soil zones are positively associated with farmland value which is reasonable, since these types of soils are the most productive soils in the Canadian Prairies (Ecological Framework of Canada). The lower productivity for the regions with brown and gray soils is confirmed by the negative sign for these dummies. Therefore, the soil zones dummies successfully show their influence on the dependent variable in the model. The year dummies are supposed to capture both observed and unobserved year fixed effects (that could be economic and environmental conditions), new rules, and all effects that vary over time. For example, the significant negative 1996 fixed effects can be a sign for occurrence of something special in this year (e.g. new rule or low economic growth) which is unobservable or is not included in our model. 5.1.5. Spatial Lag  The spatial autoregressive coefficient is estimated as 0.073 which is significant at the 0.001 level. The significant spatial lag term demonstrates that farmland value can be partly explained by neighboring farmland values, and the positive coefficient indicates that a higher farmland value in a neighbor area promotes farmland value in other areas that seems reasonable. This result confirms the necessity of incorporating a spatial lag into the Ricardian model. 5.2. Comparing the Estimates with Other Canadian Studies As was mentioned in section ?2.2, the main three studies about the Canadian Ricardian analysis are: 1) Reinsborough (2003), 2) Weber and Hauer (2003), and 3) Amiraslany (2010).  The first two studies were based on cross sectional data without market price while the third one employed panel data for the three years ___ 1991, 1996 and 2001___ for which market prices are included in the model. Thus, the current analysis is closer to? Amiraslany?s?approach (2010). Comparing to Amiraslany?s? study, the signs of all estimated marginal 56  impacts are the same except the January temperature in model 1 ___ increasing the January, April and September temperatures, and rainfall all have beneficial effects while rising the July temperature and snowfall are harmful. The Reinsborough?s?results (2003) also show that the January and April temperature have positive association with the farmland value and for the July temperature this relationship is negative which all are consistent with our results. We did not compare the September temperature because the October temperature is considered as the representative variable for fall in Reinsborough?s?paper. He also did not include other climate variables in his model. Weber and Hauer?s?study (2003) reveals that increasing the January and July temperatures are harmful and beneficial, respectively. The rainfall effect, however, is positive which is similar to our results. Excluding squared forms of climate variables would be the main reason for the difference between Weber and Hauer (2003) and the other Canadian studies??results. Besides, the estimated effects of control variables on the Canadian agriculture are the same in all studies. 57  Chapter 6: Prediction The current chapter presents a set of climate change scenarios and use them to predict the impacts of these changes on the economy of agriculture in the Canadian Prairies. Three scenarios are used to simulate the change in farmland value ___ 1) 2011-2040, 2) 2041-2070 and 3) 2071-2099. The scenarios were obtained with respect to 1971-2000 climate normals as the baseline which is the employed data in the present work. Since the grain and cattle prices are included in the model, we can involve price change scenarios in the prediction as well. After introducing the climate and price scenarios, the new values for climate variables are calculated. By using the new values, we can predict how farmland value will change in different climate and price scenarios. 6.1. Climate Change Scenarios In this section, we introduce three different scenarios under which the changes in farmland value in the future are assessed. As the climate normals are calculated for a 30-year period, the climate change scenarios are defined for such length of time too. The climate scenarios have a baseline that the potential changes are simulated base on that. For this study, the baseline is 1971-2000 climate normals that sounds perfect, as we employ exactly the climate normals of this period to solve our model. Before explaining the scenarios, note that we examine uniform temperature and precipitation scenarios for the Canadian Prairies which means every census subdivision is exposed to the same climate change. Therefore, different predictions for CSDs are the result of different sensitivities (not different scenarios). There are 24 international modelling centres that use different models to simulate the future climate. For example, Bjerknes Centre for Climate in Norway, Centre National de Recherches Meteorologiques in France, and Canadian Centre for Climate Modelling and Analysis (CCCma) in Canada develop BCM, CNRMCM and CGCM models, respectively, to predict the future climate of all points on the earth. These models run based on different emission scenarios. 58  To be consistent with the previous Canadian studies, we choose CGCM model to get the appropriate scenarios for the Canadian Prairies. One of the specifications of climate models is their ability to retrieve scenarios for every single point on the earth as well as a selected area. Thus, we select the Prairies area to get a uniform climate change scenario for this region. Choosing the model and selecting the region of interest are done in the Canadian Climate Change Scenarios Network (CCCSN) website1. To retrieve the scenarios, we use CGCM3T47 which is the last version of CGCM model. Each model can be run with different assessments and SRES2 scenarios. For the current study, we choose the fourth assessment report (AR4 2007), which is the latest one, and SRES A2 emissions scenario. The summary of A2 scenario is presented in Table ?6.1. Table ?6.1: Summary of SRES A2 Emissions Scenario Population Growth GDP Growth Energy Use Land Use Change Oil/Gas Resource Availability Technological Change Change Favoring Low Very High High Low Medium Rapid Non-Fossil Fuel Extracted July 2013 from CCCSN website CGCM3T47 model is available for the three 30-year time periods ___ 2011-2040, 2041-2070 and 2071-2099. The temperature and precipitation change scenarios in the mentioned periods are presented in Table ?6.2. The forecasts say that the average annual temperature will increase by 1.3, 2.6 and 4.1 ?C, and the annual precipitation will increase by 5%, 12% and 17%. The monthly temperature scenarios demonstrate an increase for all months where January and April will face the most and the least increases in temperature, respectively.  Figure ?6.1 was also extracted from CCCSN website and shows the modelled monthly and annual temperatures and precipitation from 2011 to 2099 by year using CGCM3T47 model.                                                  1. www.cccsn.ec.gc.ca 2. Special Report on Emissions Scenarios 59  Table ?6.2: Climate Change Scenarios for the Prairies  Change (Scenario 1) Change (Scenario 2) Change (Scenario 3) Annual Temp. (?C) 1.26 2.52 4.02 January Temp. (?C) 1.84 3.80 6.06 April Temp. (?C) 0.87 1.66 2.57 July Temp. (?C) 1.10 2.41 4.04 September Temp. (?C) 1.06 2.48 4.17 Annual Precipitation (%) 5.01 12.15 17.68 Extracted July 2013 from CCCSN website As was mentioned earlier, the present model is capable of assessing the impact of the change in market price on farmland value as well as the impact of climate change. Therefore, we need price change scenarios for the mentioned three periods There are several research in which the impact of climate change on agricultural commodity productions and prices are evaluated___Parry et al. (1999 and 2005), Darwin et al. (1995) and Adams et al., (1998). All these studies indicate that global warming will decrease the production of agricultural commodities and as a result will increase the prices. Parry et al. (1999) has predicted that output prices will rise between 3% in 2020 and 32% in 2080 due to the climate change. Following Amiraslany (2010), we consider 5%, 15% and 25% increases in the prices for the three periods. 6.2. Evaluating the Impact on Farmland Value After preparation of the required information (i.e. model estimates and climate change scenarios), we can calculate the annual change in farmland values under the three different scenarios. In fact, each scenario gives us a new set of values for climate (i.e. temperature and precipitation) and price variables. Then, by plugging the new and old values into Equation ?4.16, we can calculate the changes in the farmland values because of climate change.   60  Figure ?6.1: Modeled climate data between 2011-2099  January Temperature April Temperature   July Temperature September Temperature   Annual Temperature Annual Precipitation   Extracted July 2013 from CCCSN website 61  Table ?6.3 shows the predicted percentage and per hectare annual change in the Canadian Prairies??farmland?values?using?the three mentioned models and scenarios. According to this table, under the medium climate change, the farmland value will change 21-31 CAD/ha. These changes are 36-51 and 35-77 CAD/ha for the strong and extreme climate change, respectively. Table ?6.3: Average Annual Change in the Prairies Farmland Value  Model 1 Model 2 Model 3 Scenario 1 (Medium) 1.32% 0.9% 1.5% 31.33 CAD/ha 21.57 CAD/ha 30.98 CAD/ha Scenario 2 (Strong) 1.6% 1.71% 2.54% 38.19 CAD/ha 36.02 CAD/ha 51.65 CAD/ha Scenario 3 (Extreme) 1.44% 2.5% 3.87% 35.53 CAD/ha 51.54 CAD/ha 77.75 CAD/ha  The total annual change in farmland values in the Canadian Prairies (which can be interpreted as farm welfare) can also be calculated using the total farmland area in this region. Table ?6.4 indicates that the farmland values of the Prairies increase between 1.14-1.65 billion Canadian Dollar annually for the medium scenario. The gain in farmland value can reach $1.87-$4.1 billion for the extreme scenario. These amounts of increases are considerable compared to the annual Prairies??crop?and?animal?GDP?($11.67 billion in 2011, 2002 prices). Although all models predict that farmland value will increase by climate change, the intensity of increasing is not the same for the models. Random effects model gives us the lowest amount in the medium and strong scenarios. The pooled model estimates the largest change in scenario 1, while in scenario 2 and 3 the largest prediction belongs to the spatial random effects model which is the result of the difference in the curvature of the models.  To show the effect of incorporating price in the Ricardian model, we can do the prediction without the price change which is consistent with the approach of most Ricardian Analyses. 62  Table ?6.5 and Table ?6.6 show the predictions of change in agricultural land value with fixed prices. Table ?6.4: Annual?Change?in?the?Prairies??Farmland?Values (Farm Welfare),  (Billions of Canadian Dollar, 2002 Prices)  Model 1 Model 2 Model 3 Scenario 1 (Medium) 1.65 1.14 1.63 Scenario 2 (Strong) 2.01 1.9 2.7 Scenario 3 (Extreme) 1.87 2.71 4.1  Comparing the results of Table ?6.5 and Table ?6.6 with Table ?6.3 and Table ?6.4 shows the predicted?percentage?and?per?hectare?annual?change?in?the?Canadian?Prairies??farmland?values?using the three mentioned models and scenarios. According to this table, under the medium climate change, the farmland value will change 9-31 CAD/ha. This change is 4-51 and -2-77CAD/ha for the strong and extreme climate change, respectively. These results demonstrate a big change in the prediction of the pooled model, whereas the other models do not show a considerable change. The big marginal impact of prices in model 1 with respect to the other models is the reason of this change. Hence, in the new prediction the pooled model gives the smallest increase under the medium and strong scenarios, and interestingly a decrease under the extreme scenario in the farmland values. Table ?6.5: Average Annual Change in the Prairies Farmland Value (No Price Change)  Model 1 Model 2 Model 3 Scenario 1 (Medium) 0.31% 0.93% 1.51% 8.89 CAD/ha 20.21 CAD/ha 30.79 CAD/ha Scenario 2 (Strong) 0.08% 1.63% 2.55% 4.53 CAD/ha 33.98 CAD/ha 51.36 CAD/ha Scenario 3 (Extreme) -0.25% 2.40% 3.88% -1.87 CAD/ha 49.27 CAD/ha 77.44 CAD/ha  63  Table ?6.6: Annual Change in the Prairies??Farmland?Values (Farm Welfare), No Price Change (Billions of Canadian Dollar, 2002 Prices)  Model 1 Model 2 Model 3 Scenario 1 (Medium) 0.47 1.06 1.62 Scenario 2 (Strong) 0.24 1.79 2.71 Scenario 3 (Extreme) -0.10 2.60 4.08  As a result of different climate conditions, the impact of climate change would be different in each CSD. Representing a geographical distribution map, therefore, could disclose some facts about the climate change impact. Figure ?6.2, Figure ?6.3 and Figure ?6.4 show the percentage change of each CSD under medium, strong, and extreme scenarios, respectively. To draw these maps, we used the results of random effects model as the most fitted model (i.e. largest R-square). According to the maps, the largest changes in each province occur around the big cities (i.e. Calgary, Edmonton, Saskatoon, and Winnipeg). The north of Saskatchewan and the west of Alberta will face with the least change in farmland value due to climate change. The farmlands of these regions depreciate in value even under the medium scenario. Figure ?6.2: The percentage change in Farmland value ? RE model ? Medium Scenario    64  Figure ?6.3: The percentage change in Farmland value ? RE model ? Strong Scenario  Figure ?6.4: The percentage change in Farmland value ? RE model ? Extreme Scenario   Except for the mentioned regions in Saskatchewan and Alberta under the medium scenarios, all other CSDs gain value due to climate change under all scenarios (based on the results of Random effects approach). This analysis supports that as opposed to the other regions? like?U.S.,? climate? change? is? an?opportunity? for? the?Canadian?s?Prairies?? farmers? to?have more valuable lands.  65  6.3. Comparing the Results with the Other Canadian Studies The three Canadian Ricardian models have got totally different results for the climate change impacts. Although all studies indicate a positive association between climate change and agricultural land price, the predicted amount of gains are not the same. Using different spatial unit, empirical method, and having different scenarios can be the reason of the various predictions. Reinsborough (2003) says that the annual gain due to a climate change is only 1.5$ million for all Canada which is ignorable. The spatial unit of this study is Census Division which probably could not capture the precise impacts of climate change.  On the other hand, Weber and Hauer (2003) suggest annual benefits of 5.24$ billion for Canadian farmers which is a remarkable amount. The unit of study in this analysis is 10?10km grid which is more detailed than the Reinsborough?s?analysis?(2003).?This?can?be?the cause of having two different results. Amiraslany (2010) expresses his results in a different way. He mentioned that in 2020, 2050, 2080, climate change will push up the farmland value by 1.5%, 30% and 50% of the current price which is almost between the results of the other Canadian studies. The outcomes of present analysis are, therefore, closer to the Weber? and?Hauer?s? results (2003). The minor difference between these two studies could be because of the region of estimation, as their prediction is for all Canada not just for the Prairies. Moreover, assuming fixed market price and using different econometrics method could be the other reasons.   66  Chapter 7: Conclusion 7.1. Summary Climate change is a lasting change in the average or/and variability of climate normals that can affect many aspects of human life like health and food. Thus, this phenomenon has become a serious concern for lots of people and some governments. Clearly, one of the most vulnerable sectors against climate conditions is agriculture. Temperature, precipitation, flood, and drought are parts of climate-related factors that can highly influence agricultural production. As for the importance of the relationship between climate and agriculture, the main goal of this study is quantifying the impact of climate change in the Canadian Prairies. The Prairies is chosen as the study region, since this area has a remarkable share in the Canadian agriculture. Moreover, it is vulnerable to climate change because of high risk associated with flooding and drought. The most common method to evaluate how climate change might affect the agricultural economy is the Ricardian model. Prior to this model, researchers had been using a production function to calculate the effect of change in climate on agricultural production. This method, however, did not consider the adaptation to climate change. The Ricardian model, in fact, could deal with this problem by introducing farmland value as the response variable (instead of production) and regressing it on climatic and non-climatic variables.  After introducing the Ricardian model, a considerable number of scholars have tried to apply it in a variety of regions and also to modify the model. For example, fixed market price, which was one of the main assumptions of the Ricardian model, got relaxed by Amiraslany (2010). By evaluating the approach of including the price in the Ricardian model, we showed that the farmland value depends not only on the current market price but also the lagged prices. Hence, we added previous prices as well as current prices into the model. Furthermore, more commodity prices, compared to the Amiraslany?s?analysis,?were?incorporated to the model. 67  The other significant contribution of the present study to the literature is: using random effects and spatial random effects method to estimate the model. In the previous panel data studies, the fixed effects model had been employed to solve the Ricardian model. However, one of the requirements of using this model is that the variables of interest must be time-varying. Since the climate factors are the most important variables and as these variables are time-invariant, the fixed effects approach does not seem to be an appropriate econometrics method to estimate the model. Thus, the random effects method was used for this study. Moreover, by using spatial econometrics method, the spatial interactions between CSDs are considered which could give us a more accurate result.  Therefore, three econometrics methods have been used to estimate the Prairies Ricardian model ___ pooled WLS, random effects, and spatial panel data estimations. At first, by running two pooled WLS (one with lagged prices and the other one without them); we showed that the added lagged prices are significantly associated with the farmland value. Then, the model was estimated by the two random effects approach. Among the econometrics methods, the regular random effects had the largest R-square; however, the estimates of WLS for climate variables were more significant. The marginal impacts of climate factors show that the January, April, and September temperatures and rainfall have a positive marginal effect on the land value, whereas this relationship is negative for the July?s temperature, snowfall, and evapotranspiration. These results can confirm that the Prairies?? agriculture? is sensitive to water supplies; high July temperature leads to water scarcity, because of more evaporation during summer and as a result it has a negative effect on farmland value.  The main finding of the current analysis is that climate change is beneficial for the majority of regions in the Canadian Prairies. To obtain this result, three different climate change scenarios were applied to the estimated model. Except for the north part of Saskatchewan and the west part of Alberta in the medium climate change scenario, all other cases show increase in the farmland value. According to the results of this study, the farmlands of Canadian Prairies will gain a value between $1.14 and $4.1 billion annually (based on the estimation model and scenario).  68  The positive association between climate change and the Prairies farmland values are consistent with the previous Canadian studies. The estimated value of gains, however, are not the same among the different analyses, which can be because of using different spatial unit, data, scenarios and econometrics methods. Although this study shows that climate change is not a threat for the economy of Prairies agriculture, this phenomenon can be harmful if inappropriate adaptation strategies are adopted. Therefore, the agricultural policies have to be made to encourage farmers to utilize proper strategies and practices against climate change. These policies should help farmers to: develop better irrigation methods, choose appropriate crops, and deal with water scarcity. 7.2. Caveat The present study is subject to several limitations and caveats. The first caveat refers to the inability of the model to capture nonlinear effects of climate change on crop growth and, as a consequence, farmland value. The origin of these effects is that there are critical weather states (e.g. a critical temperature or precipitation) in which the response of crop growth to climate change will change. The mentioned nonlinearity indicates that, for example, a 1?C?increase in temperature may increase the crop growth in one CSD and decrease it in another CSD because the temperature of the second CSD is in a critical point. To deal with this problem, climate buckets can be used in the model as explanatory variables. The climate buckets refer to the number of days/hours that a climate variable is in a specific interval. For instance, the number of days that the maximum temperature is between 30 and 35 can be one bucket and the number of days that the temperature is between 25 and 30 can be another bucket. Although the possibility of incorporating the climate buckets into a Ricardian model has not been examined yet, they are included in a production function to predict yields for a variety of crops (Robertson, 2012).  The other caveat is that we might need to include other control variables in the regression model to capture the impact of changing the demand under specific circumstances. In fact, in a specific time and location, the demand for farmland may increase because people tend to purchase farmlands as the store of wealth during times of economic uncertainty?or/and as the speculative asset. Although population density can reflect some aspects of the demand, 69  including some other measures to capture the mentioned circumstances would help to have a more precise estimation. Another part of this study that needs to be taken into consideration is the climate data. As defined by the World Meteorological Organization (WMO), the climate is the average of weather elements over a 30-year time period. Thus, since the period of the data in this study is 20 years (5 census years), we considered constant climate normals for each CSD. However, it should be mentioned that if the period of available data increases to more than 30 years, using time-varying climate variables would be reasonable.  The other caveat that should be considered in this study is the existence of two distinct uncertainties: the uncertainty in the climate scenarios and the uncertainty regarding how climate change will affect crops production. Uncertainty can be an obstacle in predicting and adapting to climate change. The main sources of uncertainty in climate change scenarios ? which are extracted from GCM experiments ? are uncertainty in: 1) future emissions, 2) converting emissions to atmospheric concentrations, 3) converting concentrations to radiative forcing, 4) modelling the climate, and 5) converting model response into inputs (Mearns et al., 2001). The sources of uncertainty in the impact of climate change on crop production would be neglecting the side effects of climate change such as diseases, weeds, pests and the direct effect of greenhouse gases like carbon dioxide (Parry et al., 2004). To find out which source of uncertainty is likely the most significant one in a climate change analysis, sensitivity analysis can be used. For example, Lobell et al. (2008) evaluate the contribution of four factors: uncertainty in 1) temperature change scenario, 2) precipitation change scenario, 3) crop responses to temperature change and 4) crop responses to precipitation change. Using global data for the 94 crop?region combinations, they show that factors 1 and 3 are the main source of uncertainty for future impacts of climate change on the crop production. Quantification of uncertainty can be useful to decision makers and producers when prioritizing adaptation efforts. Using uniform climate change scenarios is the other issue that may affect the prediction. Although the utilized scenarios in this study are for the Canadian Prairies ? we did not use Canadian or Global scenarios ? using non-uniform scenarios may lead to a more accurate 70  prediction. In fact, applying uniform scenarios results in misestimating the impact of climate change in the individual CSDs. However, since the change in welfare is the summation of all changes in farmland values; and using a uniform scenario overestimates the change in farmland value for one group of CSDs and underestimates it for the other group, the impacts of two mentioned groups on farm welfare might offset each other. Therefore, the difference between the predicted change in welfare using uniform and non-uniform scenarios can be smaller than what might be expected.  Another caveat is about the spatial model. As was mentioned in Chapter 4, the spatial lag model was used to adjust the model for spatial correlation. An alternative for the spatial lag model is the spatial error model. In this model, the spatial autocorrelation between the residuals of neighboring areas is examined. To decide which model is better, we need to recognize the nature of spatial correlation (Larch et al., 2008); however, it requires several specification tests which make it complicated. Therefore, one can use well-known tests to detect the most suitable spatial model. Finally, similar to all economic analyses, the one important limitation in this study was the unavailability of the data. For example, while there are around 500 agriculture-related CSDs in the Canadian Prairies, some data were not available in more than 150 CSDs. Therefore, these CSDs were removed from the analysis which might prevent the model from capturing some important effects. Moreover, the data for some significant factors like adaptation costs, soil moisture content, irrigation, and technological change ___ which can have remarkable impacts on the farmland value ___ were not easily accessible, so they were not included in the model. 7.3. Recommendation for Future Studies Making some extension in the current study could lead to a better estimation for the economic impact of climate change on agriculture. Although data for some omitted variables (e.g. adaptation cost and technological change) are not explicitly available, researchers can define appropriate proxies for these variables and include them in the model. Examining the possibility of incorporating climate buckets as the new explanatory variables can be another attempt to improve the Ricardian approach.  71  For a more accurate prediction, non-uniform climate change scenarios can be applied to the estimated model. Since the current web-based climate model could calculate a one by one scenario for the regions, obtaining individual scenario for each CSD can be time-consuming. However, having access to an open source model may make it easier. In addition, quantification of uncertainties ? that are mentioned in the previous section ? can be done using sensitivity analysis. Knowing the relative contributions of each source of uncertainties can be helpful for making proper decisions regarding adaptations to climate change. Finally, although the market price indices are weighted for each region based on the cultivated area and number of livestock, the quality of products can cause different prices over CSDs. 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OECD.   76  Appendix: Stata printouts  WLS without lagged prices (Table 5.1)  WLS regression -  type: proportional to abs(e)  (sum of wgt is   5.3137e+04)  Linear regression                                      Number of obs =    1690                                                        F( 33,  1656) =  152.67                                                        Prob > F      =  0.0000                                                        R-squared     =  0.7813                                                        Root MSE      =  .22884  ------------------------------------------------------------------------------              |               Robust        FLVAL |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval] -------------+----------------------------------------------------------------         JANT |   -.043393    .012391    -3.50   0.000    -.0676966   -.0190894      JANT_SQ |    .018899   .0020654     9.15   0.000      .014848    .0229501         APRT |   .1829748   .0392264     4.66   0.000     .1060363    .2599134      APRT_SQ |  -.0282511     .01554    -1.82   0.069    -.0587313    .0022291         JULT |  -.1981763   .0534735    -3.71   0.000    -.3030592   -.0932934      JULT_SQ |   .0052402   .0175736     0.30   0.766    -.0292285    .0397089         SEPT |   .1747016   .0660241     2.65   0.008     .0452021    .3042012      SEPT_SQ |  -.0722455   .0279717    -2.58   0.010    -.1271091   -.0173818         RAIN |    .008628   .0006595    13.08   0.000     .0073345    .0099215      RAIN_SQ |   .0000543   5.71e-06     9.50   0.000     .0000431    .0000655         SNOW |   -.005265   .0010458    -5.03   0.000    -.0073163   -.0032138      SNOW_SQ |  -.0000231   .0000165    -1.39   0.163    -.0000555    9.37e-06        EVAPO |  -.0001654   .0000346    -4.78   0.000    -.0002333   -.0000975     EVAPO_SQ |   9.86e-08   3.89e-08     2.53   0.011     2.23e-08    1.75e-07          FFD |  -.0092356   .0034267    -2.70   0.007    -.0159567   -.0025146       FFD_SQ |   .0008987   .0001839     4.89   0.000      .000538    .0012594        BLACK |   .2614783   .0303782     8.61   0.000     .2018947     .321062        BROWN |   .0819137   .0551804     1.48   0.138     -.026317    .1901444       DBROWN |    .206194   .0407044     5.07   0.000     .1263566    .2860314         GRAY |          0  (omitted)        DGRAY |   .2032063   .0295187     6.88   0.000     .1453084    .2611043        _1991 |   .1495085   .1486581     1.01   0.315    -.1420691    .4410862        _1996 |          0  (omitted)        _2001 |   .1667334   .1144003     1.46   0.145     -.057651    .3911179        _2006 |   .3200769   .1613805     1.98   0.047     .0035456    .6366082        _2011 |   .5141995   .0896497     5.74   0.000     .3383608    .6900381    pg0_const |   .0063954   .0038166     1.68   0.094    -.0010905    .0138813    PC0_const |   4.70e-06   2.49e-06     1.89   0.059    -1.76e-07    9.58e-06          INC |   .0279042    .001922    14.52   0.000     .0241343     .031674          POP |   .1391677    .053969     2.58   0.010     .0333131    .2450223          GOV |   .9621179    .169545     5.67   0.000     .6295728    1.294663    longitude |  -.0121989   .0055849    -2.18   0.029     -.023153   -.0012448         ELEV |  -.0000509   .0002147    -0.24   0.813     -.000472    .0003702         hway |  -.0013182   .0002366    -5.57   0.000    -.0017822   -.0008542          exp |    .000693   .0000951     7.28   0.000     .0005064    .0008796        _cons |   3.456488   .7163871     4.82   0.000     2.051368    4.861608 ------------------------------------------------------------------------------    77  WLS with lagged prices (Table 5.1 & 5.2)  WLS regression -  type: proportional to abs(e)  (sum of wgt is   5.8631e+04)  Linear regression                                      Number of obs =    1690                                                        F( 42,  1647) =  137.53                                                        Prob > F      =  0.0000                                                        R-squared     =  0.8013                                                        Root MSE      =  .21973  ------------------------------------------------------------------------------              |               Robust        FLVAL |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval] -------------+----------------------------------------------------------------         JANT |  -.0284906   .0121727    -2.34   0.019    -.0523661   -.0046151      JANT_SQ |   .0171777   .0018985     9.05   0.000     .0134539    .0209015         APRT |   .1934871   .0374089     5.17   0.000      .120113    .2668612      APRT_SQ |  -.0183611   .0146299    -1.26   0.210    -.0470561     .010334         JULT |  -.1330192   .0529995    -2.51   0.012    -.2369728   -.0290656      JULT_SQ |    .025294   .0159889     1.58   0.114    -.0060667    .0566547         SEPT |   .1252387   .0636198     1.97   0.049     .0004545     .250023      SEPT_SQ |  -.0865601   .0265164    -3.26   0.001    -.1385694   -.0345508         RAIN |   .0080783   .0006216    13.00   0.000     .0068591    .0092975      RAIN_SQ |   .0000566   5.68e-06     9.95   0.000     .0000454    .0000677         SNOW |  -.0041866   .0010021    -4.18   0.000    -.0061521   -.0022211      SNOW_SQ |  -.0000237   .0000144    -1.65   0.100     -.000052    4.51e-06        EVAPO |  -.0001401   .0000337    -4.16   0.000    -.0002062    -.000074     EVAPO_SQ |   6.19e-08   3.84e-08     1.61   0.107    -1.34e-08    1.37e-07          FFD |  -.0107802   .0032615    -3.31   0.001    -.0171773    -.004383       FFD_SQ |   .0007232   .0001749     4.14   0.000     .0003802    .0010662        BLACK |   .2025315   .0291392     6.95   0.000     .1453776    .2596853        BROWN |   .0367245   .0540953     0.68   0.497    -.0693782    .1428272       DBROWN |   .1546953   .0389476     3.97   0.000     .0783033    .2310874         GRAY |          0  (omitted)        DGRAY |   .1811205   .0286719     6.32   0.000     .1248833    .2373578        _1991 |          0  (omitted)        _1996 |  -.9487694   .3856456    -2.46   0.014    -1.705177   -.1923621        _2001 |  -.0113105   .3289904    -0.03   0.973    -.6565941    .6339731        _2006 |   .6735208   .2237388     3.01   0.003     .2346783    1.112363        _2011 |  -1.204628   .3079086    -3.91   0.000    -1.808562   -.6006947    pg0_const |   .0912008   .0200362     4.55   0.000     .0519018    .1304999    pg1_const |  -.0847942   .0211171    -4.02   0.000    -.1262134    -.043375    pg2_const |   .0399754   .0075475     5.30   0.000     .0251716    .0547792    pg3_const |   .0294441   .0060946     4.83   0.000     .0174901     .041398    pg4_const |  -.0559684   .0087893    -6.37   0.000    -.0732078   -.0387291    pg5_const |    .008931   .0041021     2.18   0.030     .0008852    .0169768    PC0_const |   .0005248   .0001378     3.81   0.000     .0002546     .000795    PC1_const |    -.00077   .0002427    -3.17   0.002    -.0012459    -.000294    PC2_const |   .0002301   .0000811     2.84   0.005      .000071    .0003892    PC3_const |          0  (omitted)    PC4_const |  -.0001034   .0000603    -1.72   0.086    -.0002216    .0000148    PC5_const |   .0001347   .0000355     3.79   0.000      .000065    .0002044          INC |   .0255553   .0018417    13.88   0.000     .0219429    .0291676          POP |   .1651717   .0521315     3.17   0.002     .0629207    .2674226          GOV |   1.043952   .1724136     6.05   0.000      .705779    1.382125    longitude |  -.0101547   .0052935    -1.92   0.055    -.0205374     .000228         ELEV |  -.0001104   .0002039    -0.54   0.588    -.0005102    .0002895         hway |  -.0013151   .0002237    -5.88   0.000    -.0017538   -.0008764          exp |   .0006535   .0000914     7.15   0.000     .0004741    .0008328        _cons |   2.019406   .8649227     2.33   0.020     .3229421     3.71587 ------------------------------------------------------------------------------   78  Random Effects (Table 5.2)  note: GRAY dropped because of collinearity note: _1991 dropped because of collinearity note: PC3_const dropped because of collinearity  Random-effects GLS regression                   Number of obs      =      1690 Group variable (i): csd                         Number of groups   =       338  R-sq:  within  = 0.8837                         Obs per group: min =         5        between = 0.7419                                        avg =       5.0        overall = 0.8289                                        max =         5  Random effects u_i ~ Gaussian                   Wald chi2(42)      =  11002.15 corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000  ------------------------------------------------------------------------------        FLVAL |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+----------------------------------------------------------------         JANT |   .0720992    .028245     2.55   0.011       .01674    .1274584      JANT_SQ |   .0090051   .0028737     3.13   0.002     .0033727    .0146375         APRT |   .0511816   .0612987     0.83   0.404    -.0689615    .1713248      APRT_SQ |    .032525   .0239769     1.36   0.175    -.0144688    .0795189         JULT |  -.6475454   .0794979    -8.15   0.000    -.8033584   -.4917325      JULT_SQ |   .0189334   .0206132     0.92   0.358    -.0214678    .0593346         SEPT |   .6531537   .0982388     6.65   0.000     .4606091    .8456983      SEPT_SQ |   .0349769   .0387169     0.90   0.366    -.0409067    .1108606         RAIN |   .0059888   .0008387     7.14   0.000     .0043449    .0076327      RAIN_SQ |   .0000208   8.60e-06     2.41   0.016     3.90e-06    .0000376         SNOW |  -.0024049   .0016347    -1.47   0.141     -.005609    .0007991      SNOW_SQ |   -.000025   .0000166    -1.51   0.132    -.0000575    7.54e-06        EVAPO |  -.0003101   .0000782    -3.97   0.000    -.0004633   -.0001569     EVAPO_SQ |   1.66e-07   9.06e-08     1.84   0.066    -1.13e-08    3.44e-07          FFD |  -.0112742   .0044903    -2.51   0.012    -.0200751   -.0024733       FFD_SQ |  -.0002069   .0002552    -0.81   0.418     -.000707    .0002932        BLACK |   .3240305     .05045     6.42   0.000     .2251503    .4229107        BROWN |  -.0145118   .0972652    -0.15   0.881     -.205148    .1761245       DBROWN |   .2176425    .070393     3.09   0.002     .0796747    .3556103        DGRAY |   .2796864   .0647318     4.32   0.000     .1528144    .4065583        _1996 |  -.0079691   .1672103    -0.05   0.962    -.3356953     .319757        _2001 |   .2228253    .152957     1.46   0.145    -.0769648    .5226154        _2006 |   .3183243   .1015407     3.13   0.002     .1193082    .5173405        _2011 |   .3017674    .138476     2.18   0.029     .0303594    .5731754    pg0_const |   .0048679   .0094589     0.51   0.607    -.0136713    .0234071    pg1_const |  -.0045956   .0096392    -0.48   0.634    -.0234882    .0142969    pg2_const |   .0007752   .0037011     0.21   0.834    -.0064789    .0080292    pg3_const |   .0044026   .0031955     1.38   0.168    -.0018606    .0106657    pg4_const |  -.0161928   .0039336    -4.12   0.000    -.0239024   -.0084831    pg5_const |     .00198   .0013753     1.44   0.150    -.0007156    .0046756    PC0_const |   .0000432   .0000417     1.04   0.300    -.0000385    .0001249    PC1_const |   .0000422   .0000736     0.57   0.566     -.000102    .0001865    PC2_const |  -.0000375   .0000248    -1.51   0.130    -.0000862    .0000111    PC4_const |  -.0001776   .0000166   -10.70   0.000    -.0002101   -.0001451    PC5_const |   .0001308   9.29e-06    14.09   0.000     .0001126     .000149          INC |   .0154655   .0013236    11.68   0.000     .0128712    .0180597          POP |    .009994   .0299808     0.33   0.739    -.0487673    .0687554          GOV |   1.054627   .1489764     7.08   0.000      .762639    1.346616    longitude |   .0089439   .0080788     1.11   0.268    -.0068902     .024778         ELEV |  -.0014696   .0003047    -4.82   0.000    -.0020669   -.0008723         hway |  -.0020365   .0004014    -5.07   0.000    -.0028231   -.0012498          exp |   .0008853   .0001278     6.93   0.000      .000635    .0011357        _cons |   7.668035   .9773891     7.85   0.000     5.752387    9.583682 -------------+----------------------------------------------------------------      sigma_u |  .17395041      sigma_e |  .10157902          rho |  .74571096   (fraction of variance due to u_i) ------------------------------------------------------------------------------    79  Spatial Random Effects (Table 5.2)  note: PC5_const dropped because of collinearity note: _2011 dropped because of collinearity note: DGRAY dropped because of collinearity Iteration 0:   Log-likelihood = -4019.1729  (not concave) Iteration 1:   Log-likelihood = -2835.7061  (not concave) Iteration 2:   Log-likelihood = -2188.3896  (not concave) Iteration 3:   Log-likelihood = -695.34474  (not concave) Iteration 4:   Log-likelihood = -88.341581  (not concave) Iteration 5:   Log-likelihood =  125.76171  (not concave) Iteration 6:   Log-likelihood =  687.43164  (not concave) Iteration 7:   Log-likelihood =   759.4774  (not concave) Iteration 8:   Log-likelihood =   777.1367   Iteration 9:   Log-likelihood =  840.78612   Iteration 10:  Log-likelihood =   891.9344   Iteration 11:  Log-likelihood =  931.75327   Iteration 12:  Log-likelihood =  933.01371   Iteration 13:  Log-likelihood =  933.01842   Iteration 14:  Log-likelihood =  933.01842    SAR with random-effects                              Number of obs =      1690  Group variable: csd                               Number of groups =       338 Time variable: year                                   Panel length =         5  R-sq:    within  = 0.8869          between = 0.7909          overall = 0.8102  Log-likelihood =   933.0184 ------------------------------------------------------------------------------        FLVAL |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- Main         |         JANT |   .1112028   .0357935     3.11   0.002     .0410489    .1813567      JANT_SQ |   .0084644   .0035718     2.37   0.018     .0014639    .0154649         APRT |   .0309605   .0764563     0.40   0.686    -.1188912    .1808122      APRT_SQ |    .052295   .0300583     1.74   0.082    -.0066182    .1112082         JULT |  -.4984284   .1032105    -4.83   0.000    -.7007172   -.2961396      JULT_SQ |   .0510953   .0263124     1.94   0.052     -.000476    .1026666         SEPT |   .5195505    .124746     4.16   0.000     .2750528    .7640482      SEPT_SQ |   .0555549   .0481802     1.15   0.249    -.0388765    .1499863         RAIN |   .0045216   .0010754     4.20   0.000     .0024138    .0066293      RAIN_SQ |   .0000306   .0000109     2.82   0.005     9.34e-06    .0000519         SNOW |  -.0006885   .0020572    -0.33   0.738    -.0047206    .0033436      SNOW_SQ |  -.0000183   .0000207    -0.88   0.376    -.0000588    .0000222        EVAPO |  -.0001981      .0001    -1.98   0.047     -.000394   -2.23e-06     EVAPO_SQ |   4.99e-08   1.15e-07     0.43   0.665    -1.76e-07    2.76e-07          FFD |  -.0080059   .0056126    -1.43   0.154    -.0190064    .0029946       FFD_SQ |   -.000723   .0003328    -2.17   0.030    -.0013752   -.0000707        BLACK |     .00089   .0713969     0.01   0.990    -.1390453    .1408253        BROWN |  -.4016825    .125136    -3.21   0.001    -.6469445   -.1564205       DBROWN |  -.1215375   .0908818    -1.34   0.181    -.2996626    .0565875         GRAY |  -.2661172   .0806712    -3.30   0.001    -.4242298   -.1080045        _1991 |   -.422292    .127024    -3.32   0.001    -.6712546   -.1733295        _1996 |  -.3381949   .0878291    -3.85   0.000    -.5103367    -.166053        _2001 |  -.1771775   .1322959    -1.34   0.180    -.4364727    .0821178        _2006 |  -.1344524   .1279237    -1.05   0.293    -.3851782    .1162734    pg0_const |  -.0029721   .0086629    -0.34   0.732    -.0199511    .0140069    pg1_const |   .0025805   .0088122     0.29   0.770    -.0146911    .0198521    pg2_const |  -.0028093   .0034048    -0.83   0.409    -.0094825     .003864    pg3_const |   .0024009   .0029231     0.82   0.411    -.0033283    .0081301    pg4_const |  -.0130096   .0035993    -3.61   0.000    -.0200642   -.0059551    pg5_const |   .0015295   .0012518     1.22   0.222     -.000924    .0039831    PC0_const |   .0000656   .0000385     1.70   0.089    -9.91e-06    .0001411    PC1_const |   .0002315   .0000717     3.23   0.001      .000091    .0003719    PC2_const |  -.0007398   .0000549   -13.48   0.000    -.0008473   -.0006322    PC3_const |   .0007363   .0000489    15.05   0.000     .0006404    .0008321    PC4_const |   -.000303   .0000226   -13.42   0.000    -.0003473   -.0002588          INC |   .0134082   .0012574    10.66   0.000     .0109439    .0158726          POP |   .0053874   .0273014     0.20   0.844    -.0481224    .0588972          GOV |    1.00997   .1517263     6.66   0.000     .7125924    1.307348    longitude |   .0086629   .0100629     0.86   0.389      -.01106    .0283857 80          ELEV |  -.0017524   .0003812    -4.60   0.000    -.0024996   -.0010052         hway |  -.0018262   .0005014    -3.64   0.000    -.0028089   -.0008435          exp |   .0009555   .0001591     6.01   0.000     .0006436    .0012673        _cons |   8.435017   1.172063     7.20   0.000     6.137815    10.73222 -------------+---------------------------------------------------------------- Spatial      |          rho |    .072872   .0136451     5.34   0.000     .0461281    .0996159 -------------+---------------------------------------------------------------- Variance     |    lgt_theta |  -1.488759   .0587532   -25.34   0.000    -1.603913   -1.373604      sigma_e |   .0098601   .0003886    25.38   0.000     .0090985    .0106216 -------------+---------------------------------------------------------------- Direct       |         JANT |   .1106813   .0303641     3.65   0.000     .0511689    .1701938      JANT_SQ |   .0087328   .0038714     2.26   0.024     .0011449    .0163206         APRT |    .035785   .0764142     0.47   0.640     -.113984    .1855541      APRT_SQ |   .0524288   .0286788     1.83   0.068    -.0037806    .1086381         JULT |  -.4763132   .1046929    -4.55   0.000    -.6815076   -.2711188      JULT_SQ |    .057866   .0265932     2.18   0.030     .0057443    .1099877         SEPT |    .494952   .1275088     3.88   0.000     .2450393    .7448647      SEPT_SQ |    .046066   .0503773     0.91   0.360    -.0526717    .1448037         RAIN |   .0043735   .0010642     4.11   0.000     .0022877    .0064593      RAIN_SQ |   .0000312   9.63e-06     3.24   0.001     .0000123    .0000501         SNOW |  -.0004955   .0018105    -0.27   0.784     -.004044     .003053      SNOW_SQ |  -.0000216   .0000209    -1.03   0.302    -.0000626    .0000194        EVAPO |  -.0001959   .0001051    -1.86   0.062    -.0004019    .0000101     EVAPO_SQ |   3.33e-08   1.20e-07     0.28   0.781    -2.01e-07    2.68e-07          FFD |  -.0073144    .005406    -1.35   0.176      -.01791    .0032813       FFD_SQ |   -.000753   .0003616    -2.08   0.037    -.0014617   -.0000444        BLACK |  -.0109055   .0767236    -0.14   0.887     -.161281    .1394699        BROWN |  -.4240504   .1302218    -3.26   0.001    -.6792805   -.1688203       DBROWN |   -.138448   .0925909    -1.50   0.135    -.3199228    .0430267         GRAY |  -.2685921   .0876272    -3.07   0.002    -.4403383   -.0968459        _1991 |  -.4223126   .1174462    -3.60   0.000     -.652503   -.1921223        _1996 |  -.3322523   .0822618    -4.04   0.000    -.4934825    -.171022        _2001 |  -.1679824   .1321447    -1.27   0.204    -.4269812    .0910164        _2006 |  -.1271236   .1236322    -1.03   0.304    -.3694383    .1151911    pg0_const |  -.0032088   .0079679    -0.40   0.687    -.0188256    .0124079    pg1_const |     .00293   .0081657     0.36   0.720    -.0130745    .0189345    pg2_const |   -.002734   .0030738    -0.89   0.374    -.0087586    .0032905    pg3_const |   .0023588   .0028976     0.81   0.416    -.0033203     .008038    pg4_const |  -.0129683   .0036184    -3.58   0.000    -.0200602   -.0058764    pg5_const |   .0015705   .0014913     1.05   0.292    -.0013523    .0044934    PC0_const |   .0000699   .0000405     1.73   0.084    -9.36e-06    .0001492    PC1_const |   .0002238   .0000782     2.86   0.004     .0000704    .0003771    PC2_const |   -.000738   .0000589   -12.53   0.000    -.0008535   -.0006225    PC3_const |   .0007374   .0000484    15.24   0.000     .0006426    .0008322    PC4_const |  -.0003025   .0000239   -12.68   0.000    -.0003493   -.0002558          INC |   .0132685   .0014682     9.04   0.000      .010391     .016146          POP |     .00311   .0325795     0.10   0.924    -.0607447    .0669647          GOV |   1.018914   .1584096     6.43   0.000     .7084368    1.329391    longitude |   .0090294    .011695     0.77   0.440    -.0138925    .0319512         ELEV |  -.0017494   .0003611    -4.84   0.000    -.0024572   -.0010416         hway |  -.0018205   .0005137    -3.54   0.000    -.0028274   -.0008136          exp |   .0009682   .0001396     6.94   0.000     .0006947    .0012418 -------------+---------------------------------------------------------------- Indirect     |         JANT |   .0048593    .001609     3.02   0.003     .0017057    .0080129      JANT_SQ |   .0003871   .0001925     2.01   0.044     9.73e-06    .0007644         APRT |   .0016865   .0036493     0.46   0.644     -.005466     .008839      APRT_SQ |   .0023371   .0014267     1.64   0.101    -.0004592    .0051333         JULT |  -.0206405   .0052153    -3.96   0.000    -.0308623   -.0104187      JULT_SQ |   .0026033   .0013889     1.87   0.061    -.0001188    .0053255         SEPT |   .0213788   .0058619     3.65   0.000     .0098896    .0328679      SEPT_SQ |   .0019904     .00223     0.89   0.372    -.0023804    .0063611         RAIN |   .0001892   .0000485     3.90   0.000     .0000941    .0002844      RAIN_SQ |   1.38e-06   5.20e-07     2.65   0.008     3.59e-07    2.40e-06         SNOW |  -.0000194   .0000795    -0.24   0.808    -.0001751    .0001364      SNOW_SQ |  -9.53e-07   9.38e-07    -1.02   0.309    -2.79e-06    8.84e-07        EVAPO |  -8.29e-06   4.36e-06    -1.90   0.057    -.0000168    2.60e-07     EVAPO_SQ |   1.30e-09   5.26e-09     0.25   0.805    -9.01e-09    1.16e-08          FFD |  -.0003185   .0002427    -1.31   0.189    -.0007942    .0001572       FFD_SQ |  -.0000337   .0000181    -1.86   0.063    -.0000692    1.85e-06        BLACK |  -.0005848   .0035348    -0.17   0.869     -.007513    .0063433        BROWN |  -.0187518   .0071487    -2.62   0.009     -.032763   -.0047405       DBROWN |  -.0061859   .0044021    -1.41   0.160    -.0148139    .0024422         GRAY |   -.011805   .0046191    -2.56   0.011    -.0208584   -.0027516        _1991 |  -.0186559   .0065773    -2.84   0.005    -.0315471   -.0057646        _1996 |  -.0146095   .0045333    -3.22   0.001    -.0234945   -.0057245        _2001 |  -.0075269   .0060399    -1.25   0.213    -.0193649    .0043111 81         _2006 |  -.0058038   .0056464    -1.03   0.304    -.0168705     .005263    pg0_const |   -.000151   .0003683    -0.41   0.682    -.0008729    .0005709    pg1_const |   .0001376   .0003783     0.36   0.716    -.0006039    .0008791    pg2_const |  -.0001247   .0001414    -0.88   0.378    -.0004018    .0001524    pg3_const |   .0000994   .0001255     0.79   0.428    -.0001466    .0003454    pg4_const |  -.0005631   .0001748    -3.22   0.001    -.0009058   -.0002204    pg5_const |   .0000683    .000064     1.07   0.286    -.0000571    .0001938    PC0_const |   3.06e-06   1.83e-06     1.67   0.096    -5.37e-07    6.65e-06    PC1_const |   9.80e-06   3.83e-06     2.56   0.010     2.30e-06    .0000173    PC2_const |  -.0000323   6.27e-06    -5.15   0.000    -.0000446     -.00002    PC3_const |   .0000323   6.07e-06     5.31   0.000     .0000204    .0000442    PC4_const |  -.0000132   2.55e-06    -5.20   0.000    -.0000182   -8.25e-06          INC |   .0005786   .0001106     5.23   0.000     .0003618    .0007953          POP |   .0001071   .0013877     0.08   0.938    -.0026128    .0028271          GOV |   .0444219   .0097415     4.56   0.000     .0253289    .0635149    longitude |    .000409   .0005253     0.78   0.436    -.0006206    .0014386         ELEV |  -.0000771   .0000227    -3.40   0.001    -.0001216   -.0000326         hway |  -.0000802   .0000287    -2.79   0.005    -.0001364   -.0000239          exp |   .0000425   .0000104     4.08   0.000     .0000221    .0000629 -------------+---------------------------------------------------------------- Total        |         JANT |   .1155407   .0317376     3.64   0.000     .0533361    .1777453      JANT_SQ |   .0091198   .0040523     2.25   0.024     .0011774    .0170623         APRT |   .0374715   .0799747     0.47   0.639     -.119276    .1942191      APRT_SQ |   .0547658   .0300339     1.82   0.068    -.0040996    .1136313         JULT |  -.4969537   .1082728    -4.59   0.000    -.7091644   -.2847429      JULT_SQ |   .0604693   .0279078     2.17   0.030     .0057711    .1151675         SEPT |   .5163308   .1318087     3.92   0.000     .2579905     .774671      SEPT_SQ |   .0480564   .0525469     0.91   0.360    -.0549337    .1510464         RAIN |   .0045627   .0010989     4.15   0.000      .002409    .0067164      RAIN_SQ |   .0000326   .0000101     3.22   0.001     .0000128    .0000524         SNOW |  -.0005148   .0018891    -0.27   0.785    -.0042174    .0031877      SNOW_SQ |  -.0000226   .0000218    -1.03   0.302    -.0000654    .0000202        EVAPO |  -.0002042   .0001091    -1.87   0.061     -.000418    9.66e-06     EVAPO_SQ |   3.46e-08   1.25e-07     0.28   0.781    -2.10e-07    2.79e-07          FFD |  -.0076329   .0056376    -1.35   0.176    -.0186824    .0034166       FFD_SQ |  -.0007867   .0003787    -2.08   0.038    -.0015289   -.0000445        BLACK |  -.0114904   .0802202    -0.14   0.886    -.1687191    .1457384        BROWN |  -.4428022   .1365765    -3.24   0.001    -.7104872   -.1751171       DBROWN |  -.1446339   .0968427    -1.49   0.135    -.3344421    .0451743         GRAY |  -.2803971    .091743    -3.06   0.002    -.4602101    -.100584        _1991 |  -.4409685   .1232311    -3.58   0.000    -.6824971   -.1994399        _1996 |  -.3468617    .086066    -4.03   0.000     -.515548   -.1781755        _2001 |  -.1755093   .1380172    -1.27   0.203     -.446018    .0949994        _2006 |  -.1329274   .1291643    -1.03   0.303    -.3860847      .12023    pg0_const |  -.0033598   .0083304    -0.40   0.687    -.0196872    .0129675    pg1_const |   .0030676   .0085382     0.36   0.719    -.0136669    .0198021    pg2_const |  -.0028588   .0032125    -0.89   0.374    -.0091552    .0034377    pg3_const |   .0024582   .0030194     0.81   0.416    -.0034597    .0083762    pg4_const |  -.0135314    .003758    -3.60   0.000     -.020897   -.0061658    pg5_const |   .0016389   .0015536     1.05   0.291    -.0014061    .0046838    PC0_const |    .000073   .0000422     1.73   0.084    -9.69e-06    .0001556    PC1_const |   .0002336   .0000816     2.86   0.004     .0000735    .0003936    PC2_const |  -.0007703   .0000617   -12.48   0.000    -.0008913   -.0006493    PC3_const |   .0007697   .0000507    15.18   0.000     .0006703    .0008691    PC4_const |  -.0003158   .0000249   -12.66   0.000    -.0003647   -.0002669          INC |   .0138471   .0015134     9.15   0.000     .0108808    .0168134          POP |   .0032171   .0339481     0.09   0.925    -.0633199    .0697541          GOV |   1.063336   .1640805     6.48   0.000      .741744    1.384928    longitude |   .0094384   .0122078     0.77   0.439    -.0144884    .0333652         ELEV |  -.0018265   .0003793    -4.81   0.000      -.00257    -.001083         hway |  -.0019007   .0005387    -3.53   0.000    -.0029566   -.0008448          exp |   .0010107   .0001467     6.89   0.000     .0007231    .0012983 ------------------------------------------------------------------------------  

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