Drew Behnke Food and Agriculture Organization of the United Nations UC Berkeley and UC Santa Barbara

Transcription

1 Lecture 3: Using Regression Analysis to Model Climate Risk Training Course on Economic Assessment Methods for Policy Support of Climate Change Adaptation in the Agricultural Sector in Lao PDR Drew Behnke Food and Agriculture Organization of the United Nations UC Berkeley and UC Santa Barbara NAFRI Vientiane, Lao PDR August, 2014

2 Contents 1. Overview of Regression Techniques 2. Overview of Panel Data and Panel Regression 3. Types of Climate Regressions 4. Projecting results Behnke 2

3 Regression Analysis Statistical tool to study the relationship(s) between two or more economic variables. Example: Relationship between rice yields and temperature. Let Y d = Yield for district d Let X d = Average temperature district d Form the regression model that estimates the relationship: Y d =β 1 +β 2 X d +u d Behnke 3

4 Regression Analysis Missing many important variables from previous model (soil quality, fertilizer use, precipitation, etc.) that we may not have data for. This is known as Omitted Variable Bias. Panel data and panel regression techniques can provide a solution to omitted variable bias. Behnke 4

5 Panel Regressions Panel data is repeated observations on same cross sectional unit d. Typically this is simply adding a time component (e.g. yearly district yields). Therefore our previous model becomes: Y dt =β 1 +β 2 X dt +u dt where t represents year Behnke 5

6 Panel Regressions Fixed effects allow consistent estimation of our parameter of interest when the unobserved variables are correlated with explanatory variable (X dt ). The basic idea of fixed-effects is to transform the data to eliminate the unobserved effect. There are many ways to do this, but typically individual dummy variables are added to the model. Behnke 6

7 Panel Regressions Example: Suppose there are systematic differences between two districts in the production of rice that we do not observe (soil quality for example). This can be expressed as: E[u dt d is district 1] = 0 E[u dt d is district 2] = µ u Adding a dummy variable for district 2 will remove the bias! Y dt =β 1 + β 2 X dt + µ u D d + (u dt µ u D d ) E[u dt µ u D d ] = 0 for both districts Behnke 7

8 Panel Regressions In Summary: Panel data allows the use of fixed effects. With unobservable data the traditional approach is to view the unobserved data as parameters to be estimated by the model. If there are systematic differences across districts we include a dummy for each district to hold these effects constant. Behnke 8

9 Climate Regressions We utilize the presumably random year-to-year variation in temperature and precipitation to estimate whether rice yields are higher or lower in years that are warmer and wetter. We begin with an approach of estimating the effects of climate on rice yields using a panel regression with a single growing season metric for each weather covariate (average min T, max T, and precipitation across the growing season). Using average seasonal conditions, we estimate a linear model for each rice production system. These are later used to predict yields under various climate scenarios. Behnke 9

10 Climate Regressions By using fixed effects, district specific deviations in weather from the district averages are used to identify the effect of weather on yields. We select district and year fixed effects for our analysis. District fixed effects control for any unobservable characteristic that varies across district but is constant over time. This accounts for important differences across districts such as soil conditions or areas with a higher prevalence of intensive production systems. Year fixed effects control for any unobservable characteristic that varies across years but is constant across all districts. This includes national time trends such as improved technology (irrigation, fertilizer use, or the introduction of improved seed varieties for example). Behnke 10

11 Climate Regressions We know that there are many factors that affect crop yields, including soil quality, technology, agrochemicals, endogenous behavior, etc. Here, we are only considering the impact of weather, while the other factors are unobserved by us. If district-level time-series data were available on other factors such as agricultural investment, fertilizer use, or pesticides, then we could include these explanatory variables in our model. The fixed effects model attempts to control for these unobserved factors, so that we can still produce unbiased estimates of climate effects. Behnke 11

12 Climate Regressions In other words, we can control for a variety of unobserved characteristics but cannot estimate them in our model. We are not attempting to explain every factor that affects yields, but merely to identify the effect of temperature and rainfall. Given our interest is ultimately how yields will change in the face of new climate conditions this does not affect our analysis. Behnke 12

13 Climate Regressions The following reduced form model is our primary empirical specification. Equation 1: Panel Model of Average Weather Effects log(y dt ) = β 1 MinT dt + β 2 MaxT dt + β 3 P + γ d + α t + ε dt Y dt is yield for district d in year t. The model includes district fixed effects γ d and year fixed effects α t. β 1-3 represent the coefficients on our weather variables Behnke 13

14 Results Behnke 14

15 Climate Regressions The previous model is linear which assume that effects of weather are the same over different ranges. For example, the linear model assumes an increase in maximum temperature from 29 to 30 has the same effect as an increase from 33 to 34 (which is likely incorrect). We would like to estimate a piece-wise linear model that relaxes this assumption by estimating different slopes over different ranges of temperatures. Behnke 15

16 Climate Regressions With more data we might run the following model: log(y dt ) = β 1 (MinT dt )(I MinTdt < C min ) + β 2 (MinT dt C min )(I MinTdt > C min ) + β 3 (MaxT dt )(I MaxTdt < C max ) + β 4 (MaxT dt C max )(I MaxTdt > C max ) + β 5 (Pr dt )(I Prdt < C pr ) + β 6 (Pr dt C pr )(I Prdt > C Pr ) + γ d + α t ε dt Behnke 16

17 Climate Regressions Behnke 17

18 Climate Regressions A more flexible estimation technique utilizes equally spaced temperature bins. Each bin counts the number of days over the course of the year that falls into some category. Behnke 18

19 Climate Regressions Behnke 19

20 Projections How can we project future yield effects? 1. Use statistical models with historical data to model the yield-climate relationship. 2. Use GCM projections to estimate future climate conditions 3. Evaluate the statistical model at future years under climate change scenarios 4. Evaluate the statistical model at future years under no climate change scenario (e.g., historical averages) 5. The difference between future yields under climate change and future yields under no change is an estimate of the impact of climate change on yields Behnke 20

21 Projections Unclear whether any GCM model is more valid than others. Predicted yields depend highly on which GCM is used to forecast climate conditions. We include as many models as possible with equal weights. Predictions can be very wide, but policy recommendations based on a single model seem unwise. 14 models under 3 different economic scenarios (42 total) Calculate median outcomes for each model assuming low, medium, or high emissions. Behnke 21

22 Projections How can we project future yield effects? If we compare future yields under cc to current yields then we are assuming that yields there will be no technological improvement in the future. o It would be like saying yields in 10 years will be the same as yields right now if the temperature and rainfall are the same. We need to compare future yields under cc to future yields under no cc. o We can simulate no cc by using our yield model to account for technological trend while assuming no cc is equivalent to average historical conditions This makes for a more realistic comparison Behnke 22

23 Climate Regressions yield cc current conditions C A B C-A < 0 = Future yields under cc vs Future yields under no cc right wrong A B > 0 = Future yields under cc vs Current yields past present future year Behnke 23

24 Questions? Behnke 24