text: *! version 1.0.0 13Jul2020 //----------------------------------------------------------------------------- // // mivcausal - Testing the hypothesis about the signs of the 2SLS weights // Test by Cox and Shi (2019) // //----------------------------------------------------------------------------- capt program drop mivcs program mivcs, rclass version 10.0 syntax [anything] [if] [in] // Step 1 - Solving the quadratic program * Obtain the matrix inverse mat sigmainv = inv(Zcov) * Solve the quadratic program by calling the Mata function mat thetahat = thetaols[1..1,.]' mata: x = cskkt("sigmainv", "thetahat") * Retrieve the results scalar cstest_temp = r(obj) scalar csdf = r(thetazero) if string(csdf) == "Error" { exit 498 } * Compute the test statistic from the minimized value scalar cstest = NN * cstest_temp // Step 2 - Compute the p-value if chi2(csdf, cstest) == . { scalar pvtemp = 0 } else { scalar pvtemp = chi2(csdf, cstest) } // Step 3 - Return the p-value return scalar pval_cs = 1 - pvtemp end //----------------------------------- // Mata function //----------------------------------- version 10.0 mata: mata clear // Mata function 1: To solve the linear program that resulted from the KKT // conditions of the quadratic program mata: void cskkt(string scalar sigmainvmat, string scalar thetamat) { // Step 1 - Make matrix sigmainv = st_matrix(sigmainvmat) theta = st_matrix(thetamat) // Step 2 - Extract the matrix information s11 = sigmainv[1,1] s12 = sigmainv[1,2] s22 = sigmainv[2,2] theta1 = theta[1,1] theta2 = theta[2,1] // Step 3 - Solve the quadratic program // Case 1: s1 > 0 and s2 > 0 if (theta1 >= 0 & theta2 >= 0) { s1 = theta1 s2 = theta2 nk = 0 } else { // Case 2: s1 > 0 and s2 = 0 lambda2 = -2 * (s22 - (s12^2/s11)) * theta2 s1 = theta1 + (s12/s11) * theta2 if (lambda2 >= 0 & s1 > 0) { s2 = 0 nk = 1 } else { // Case 3: s1 = 0 and s2 > 0 lambda1 = -2 * (s11 - (s12^2/s22)) * theta1 s2 = theta2 + (s12/s22) * theta1 if (lambda1 >= 0 & s2 > 0) { s1 = 0 nk = 1 } else { // Case 4: s1 = 0 and s2 = 0 lambda1 = -(2 * s11 * theta1 + 2 * s12 * theta2) lambda2 = -(2 * s22 * theta2 + 2 * s12 * theta1) if (lambda1 >= 0 & lambda2 >= 0) { s1 = 0 s2 = 0 nk = 2 } else { nk = "Error" } } } } // Step 4 - Solve the optimal value // Assign t matrix that is resulted from the optimization problem t1 = - s1 t2 = - s2 tstar = (t1 \ t2) // Step 5 - Compute the objective value pt = theta + tstar objval = pt' * sigmainv * pt // Step 6 - Return results st_numscalar("r(obj)", objval) st_numscalar("r(thetazero)", nk) } end
explanation: The provided text is a Stata program that implements a statistical test for the hypothesis about the signs of 2SLS (Two-Stage Least Squares) weights, as described by Cox and Shi (2019). The program includes both Stata and Mata code to solve a quadratic program and compute a test statistic and p-value. The text does not contain a math question or an answer to a math question.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: *! version 1.0.0 13Jul2020 //----------------------------------------------------------------------------- // // mivcausal - Testing the hypothesis about the signs of the 2SLS weights // Test by Cox and Shi (2019) // //----------------------------------------------------------------------------- capt program drop mivcs program mivcs, rclass version 10.0 syntax [anything] [if] [in] // Step 1 - Solving the quadratic program * Obtain the matrix inverse mat sigmainv = inv(Zcov) * Solve the quadratic program by calling the Mata function mat thetahat = thetaols[1..1,.]' mata: x = cskkt("sigmainv", "thetahat") * Retrieve the results scalar cstest_temp = r(obj) scalar csdf = r(thetazero) if string(csdf) == "Error" { exit 498 } * Compute the test statistic from the minimized value scalar cstest = NN * cstest_temp // Step 2 - Compute the p-value if chi2(csdf, cstest) == . { scalar pvtemp = 0 } else { scalar pvtemp = chi2(csdf, cstest) } // Step 3 - Return the p-value return scalar pval_cs = 1 - pvtemp end //----------------------------------- // Mata function //----------------------------------- version 10.0 mata: mata clear // Mata function 1: To solve the linear program that resulted from the KKT // conditions of the quadratic program mata: void cskkt(string scalar sigmainvmat, string scalar thetamat) { // Step 1 - Make matrix sigmainv = st_matrix(sigmainvmat) theta = st_matrix(thetamat) // Step 2 - Extract the matrix information s11 = sigmainv[1,1] s12 = sigmainv[1,2] s22 = sigmainv[2,2] theta1 = theta[1,1] theta2 = theta[2,1] // Step 3 - Solve the quadratic program // Case 1: s1 > 0 and s2 > 0 if (theta1 >= 0 & theta2 >= 0) { s1 = theta1 s2 = theta2 nk = 0 } else { // Case 2: s1 > 0 and s2 = 0 lambda2 = -2 * (s22 - (s12^2/s11)) * theta2 s1 = theta1 + (s12/s11) * theta2 if (lambda2 >= 0 & s1 > 0) { s2 = 0 nk = 1 } else { // Case 3: s1 = 0 and s2 > 0 lambda1 = -2 * (s11 - (s12^2/s22)) * theta1 s2 = theta2 + (s12/s22) * theta1 if (lambda1 >= 0 & s2 > 0) { s1 = 0 nk = 1 } else { // Case 4: s1 = 0 and s2 = 0 lambda1 = -(2 * s11 * theta1 + 2 * s12 * theta2) lambda2 = -(2 * s22 * theta2 + 2 * s12 * theta1) if (lambda1 >= 0 & lambda2 >= 0) { s1 = 0 s2 = 0 nk = 2 } else { nk = "Error" } } } } // Step 4 - Solve the optimal value // Assign t matrix that is resulted from the optimization problem t1 = - s1 t2 = - s2 tstar = (t1 \ t2) // Step 5 - Compute the objective value pt = theta + tstar objval = pt' * sigmainv * pt // Step 6 - Return results st_numscalar("r(obj)", objval) st_numscalar("r(thetazero)", nk) } end
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a Stata program that implements a statistical test for the hypothesis about the signs of 2SLS (Two-Stage Least Squares) weights, as described by Cox and Shi (2019). The program includes both Stata and Mata code to solve a quadratic program and compute a test statistic and p-value. The text does not contain a math question or an answer to a math question.
  
  Label: no-question