1. SCENARIO #1: Housing Bubble Bursts  Negative shock in real estate sector: -18%  Most affected sectors through comparison of expected GDP without shock: Real Estate, Retail Trade, Wholesale Trade Economic Network Model: Forecast of Cascading Shocks Team 8: Robert Feigenberg, Jungsun Kim, Carolina Lee, Daniela Savoia ABSTRACT The United States economy can be modeled as an interconnected network made up of various sectors. The connections between sectors determine the network structure and the influence levels of each sector on the rest of the economy. The sector relationships are determined by the use of one sector’s output as another sector’s input. When a shock, or a large change in expected output, occurs in a given sector, the effect of the disturbance is experienced throughout the entire economy. It is a useful tool to forecast the magnitude and spread of the effects of a shock over time. Our approach for forecasting the shock effects in an economy is to determine the network structure and connections between sectors. A mathematical model is used to measure the random noise in the economy and differentiate it from a larger shock in the economy. Using this model, the effects of an individual shock are forecasted and simulated over time. The model’s accuracy is verified with data on past shocks in the US economy. The model visually displays the network structure in a diagram and a table, highlighting the central and most influential sectors in the economy. The forecasted effects of a shock are simulated over time and demonstrated graphically. The final product design is an application that allows users to input the origin and magnitude of a shock and analyze its forecasted effects throughout the economy. ADVISORS Dr. Alejandro Ribeiro Dr. Ali Jadbabaie DEMO TIMES Thursday, April 21, 2011 9:00-9:30 AM | 2:30-4:00 PM Special Thanks To Dr. Ken Laker Dr. Peter Scott Dr. Raymond Watrous Objectives UNIVERSITY OF PENNSYLVANIA SCHOOL AND ENGINEERING AND APPLIED SCIENCE Department of Electrical and Systems Engineering Design a model to forecast change in output in the next period given knowledge of the historical level of output Forecast the effects of large initial disturbances Implement and validate the model based on historical data Create an interactive user-friendly Graphical User Interface (GUI) where a user can input specific details about the shock of interest and observe the forecasted effect across sectors Network Diagram of the U.S. Economy Figure 1 shows that all 61 sectors of the U.S. economy are highly interconnected. Due to such intricate relationship among the sectors, economic shock in one sector propagates through other sectors. Figure 2 highlights sectors with higher degree of connectivity. The cascading effect is greater when the shocks occur in more- connected sectors. Simulation Results of Potential Economic Shocks Figure 1. U.S. Economy at All Levels of Connectivity Figure 2. U.S. Economy with Input-Output Proportion > 10% “Richter” Scale of Shock Magnitude (In percent change of output) 6%: “British Petroleum Oil Spill” 18%: “Technology Bubble Burst” 30%: “Subprime Mortgage Crisis” Model Determination ε ~ N(μ, Σ) Average μ was calculated using a sample mean of the observed ε The sample covariance matrix Σ was calculated using the following equation where Σ is the sample mean of Σ(t) Σ(t) = X(t+1) / V*A*X(t) There is a correlation between the terms in ε making a linear eigenvalue decomposition approach necessary The eigenvalues were computed and summed to determine the principal values of the system As 10 eigenvalues represent 99% of the system’s randomness, the U.S. economy has 10 degrees of freedom Σ = UDU T where U = Matrix with eigenvectors as columns [61 x 10] D = Diagonal matrix with eigenvalues [10 x 10] It is possible to model ε By using the decomposition of Σ, ε = μ + Σ 1/2 δ = μ + UD 1/2 δ where δ ~ N(0,1) V = Value Added Matrix [61 x 61] Stationary diagonal matrix that represents the proportion of output from 61 sectors that are used as final goods Each entry was computed by subtracting intermediate goods from the total output per sector V(t) = X(t+1)/(A*X(t)) V is the average of V(t) for the years 1987 to 2009 A = Input-Output Matrix [61 x 61] Matrix that represents proportion of intermediate good of one sector used as inputs as the other sectors Row sum is 1 for all sectors Calculated from Bureau of Economic Analysis (BEA) data from 1998 to 2008 Example Input-Output Matrix for a simple economy: 70% of Sector 1’s output at time t serves as an input to Sector 1 at time t+1 10% of Sector 2’s output at time t serves as an input to Sector 2 at time t+1 Mathematical Representation of the Model X(t) = Output vector at time t [61 x 1] Historical data is available from the Bureau of Economic Analysis (BEA) from 1987 to 2009 Data is measured annually Forecasted output after 2009 is derived from the model ε(t) = Noise vector at time t [61 x 1] Modeled as a Colored (Non-White) Gaussian Distribution using historical data ε ~ N(μ,Σ) where μ and Σ were calculated using observed data μ is the average vector [61 x 1] Σ is the covariance matrix [61 x 61] Probability distribution function (pdf) of ε the farms sector for 2010 without any external shocks: System Diagram A V X(t+1 ) ε (t ) Delay X(t ) To validate our model, we further observed the principle components of our empirical covariance matrix Σ An out-of-sample Average μ was calculated using a sample mean of the observed ε Principal component analysis was applied to generate a matrix out-of-sample data that should approach a normal: (Σ -1/2 ) T *(ε(t) – μ)≈ N(0,1) The result: 7 of our 10 principal components passed the following Chi-Squared test of our data versus a standard normal: H 0 : The sampled data comes from our specified distribution and X 2 = ∑ (N i -npi)2/npi Figure 5 is a normal probability plot, plotting our out-of-sample data vs. a standard normal random variable. This visually confirms that the majority of the principal component data follows a normal distribution: Model Validation Figure 3. Sample Input- Output Matrix Figure 4. Probability distribution function for farms sector in 2010 Figure 5: Block Diagram Figure 6: Normal Probability Plot SCENARIO #2: Spike in Construction Output  Positive shock in construction sector: +6%  Most affected sectors through comparison of expected GDP without shock: Real Estate, Utilities Retail Trade Figure 7: Real Estate Sector Output Over Time with Upper/Lower Forecast Bounds and Expected GDP Figure 8: Construction Sector Output Over Time with Upper/Lower Forecast Bounds and Expected GDP