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From |
Eilya Torshizian <[email protected]> |

To |
"[email protected]" <[email protected]> |

Subject |
st: Reporting statistics for manipulated coefficients in a 2SLS design |

Date |
Thu, 16 Jan 2014 22:32:27 +0000 |

Dear Statalist members, I need to serve a semi two stage least squares (TSLS) in which the coefficients of the second stage are manipulated. Here I am going to present a very short and simplified version of the estimations. I am going to estimate the effect of government expenditure (G) on GDP. The components of GDP are consumption (C), Investment (I) and government expenditure (G), so GDP = f(C, I, G). In my estimations, C and I are instrumented by G and another variable (let's call it Variable1). Thus, first stage regressions are as follows, 1.1: C = bc1*VAR1 + bc2*G C: Consumption VAR1: variable 1 G: Government expenditure bc1, bc2: coefficients 1.2: I = bi1*VAR1 + bi2*G VAR1: variable 1 G: Government expenditure bi1, bi2: coefficients In the second stage I need to put the total of the first stages' coefficients in the equation. Then I only need to report p_values and other statistics based on the total coefficients derived from the first stage, i.e. I am not going to estimate anything in the second stage. The second stage's equation is as follows, 2: GDP = (bc1 + bi1)*VAR1 + (1 + bc2 + bi2) * G The code that I have attached below worries me from two aspects. First, I doubt if the replacement of coefficients in the second stage is done correctly? Second, I am not sure if the standard errors are biased or not? The code is as follows: *VARIABLES and MULTIPLIERS are written in capital letters *Loading the dataset use "StataSheet.dta", clear *Declare time-series settings tsset YEAR *First Stage Consumption regression (1.1) regress C VAR1 G gen BC1 = _b[VAR1] gen BC2 = _b[G] *First Stage Investment regression (1.2) regress I VAR1 G gen BI1 = _b[VAR1] gen BI2 = _b[G] *Summing up the coefficients derived from the first stages gen BT1 = BC1 + BI1 gen BT2 = BC2 + BI2 *Second Stage regression regress Y VAR1 G *Here I am trying to get rid of the biased Standard errors. However, I am not sure if I need to do this! predict double RES, residual replace RES = RES^2 quietly summ RES scalar RMSE = r(mean)*r(N)/e(df_r) matrix VM = e(V) matrix VM = e(V) * RMSE / e(rmse)^2 *I replace the coefficients by the total coefficients derived from the first stage matrix M = e(b) matrix M[1,1] = BT1 matrix M[1,2] = 1 + BT2 *I doubt if I am right here. I need to replace the coefficient matrix with the manipulated coefficient matrix (M). ereturn post M VM, noclear *Saving the results for the second stage (2), estimates store EST1 *Run a Wald test of the equality of the replaced coefficients test VAR1 G *END Please let me know if my question needs further clarifications. Thanks, Eilya. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

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