Modeling Shocks in COVID 19 with Stochastic Differential EquationsĤ7. Modeling COVID 19 with Differential EquationsĤ5. Optimal Savings III: Occasionally Binding ConstraintsĤ4. Consumption and Tax Smoothing with Complete and Incomplete MarketsĤ1. Optimal Savings I: The Permanent Income ModelĤ0. Optimal Growth III: The Endogenous Grid Methodģ8. Optimal Growth I: The Stochastic Optimal Growth Modelģ6. A Problem that Stumped Milton Friedmanģ2. Krylov Methods and Matrix ConditioningĢ8. Numerical Linear Algebra and FactorizationsĢ0. Orthogonal Projections and Their Applicationsġ9. Geometric Series for Elementary Economicsġ6. Packages, Testing, and Continuous Integrationġ4. GitHub, Version Control and Collaborationġ2. Solvers, Optimizers, and Automatic Differentiationġ1. Introduction to Types and Generic Programmingĩ. Arrays, Tuples, Ranges, and Other Fundamental Typesĥ. A = then x = reshape(A, 4) turns it into a vector. Hint: Convert the matrix to a vector to use fixedpoint. Redo Exercise 1 using the fixedpoint function from NLsolve this lecture.Ĭompare the number of iterations of the NLsolve’s Anderson Acceleration to the handcoded iteration used in Exercise 1. Plot a histogram of these estimates for each variable. Into matrices and vectors, and directly use the equations forįor each of the M=20 simulations, calculate the OLS estimates for \(a, b, c, d, \sigma\). Repeat that so you have M = 20 different simulations of the y for the N values.įinally, calculate order least squares manually (i.e., put the observables Where \(y, x_1, x_2\) are scalar observables, \(a,b,c,d\) are parameters to estimate, and \(w\) are iid normal with mean 0 and variance 1.įirst, let’s simulate data we can use to estimate the parametersĭraw \(N=50\) values for \(x_1, x_2\) from iid normal distributions.ĭraw a \(w\) vector for the N values and then y from this simulated data if the parameters were \(a = 0.1, b = 0.2 c = 0.5, d = 1.0, \sigma = 0.1\). The value nothing is a single value of type Nothing Missing (“data scientists null”): used when a value would make conceptual sense, but it isn’t available.Ĥ.6.1. Nothing (“software engineers null”): used where no value makes sense in a particular context due to a failure in the code, a function parameter not passed in, etc. There are two distinct use cases for this Sometimes a variable, return type from a function, or value in an array needs to represent the absence of a value rather than a particular value. e.g., param_gen = (alpha = 0.1, beta = 0.2) would be roughly equivalent to the above. You can also use the in the Parameters.jl package, which automatically creates a function. Nothing and Basic Error HandlingĪn alternative approach, defining a new type using struct tends to be more prone to accidental misuse, leads to a great deal of boilerplate code, and requires a julia restart after every update.
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