# bma -- Determinants of Horizontal Spillovers from FDI: Evidence from a Large Meta-Analysis # Havranek & Irsova, World Development 42(1), 2013. Reproduces Table 4 ("Test of publication # bias") plus the paper's headline numbers: the average spillover, and the Table 2 OLS # "frequentist check" rows for the technology gap and ownership structure. # # ------------------------------------------------------------------------------------------ # What Table 4 actually estimates # ------------------------------------------------------------------------------------------ # The table's note says the model was "estimated by weighted least squares with the precision # (the inverse of standard error) taken as the weight." The author's own published do-file # (site/bma/determinants.do) does not write that as an explicit aweighted regression of e on # se. It precomputes prec = 1/se (line 17) and, after xtset idstudy, runs # # xtreg t prec, fe vce(cluster idstudy) (determinants.do line 136) # xi: xtreg t prec i.idcountry, fe vce(cluster idstudy) (determinants.do line 137) # # where t is the study's own t-statistic (e/se), already a column in the published data. # Dividing e = b0 + b1*se + u through by se gives t = b0*(1/se) + b1 + u/se, so an OLS # regression of t on prec IS the precision-weighted regression of e on se, run without ever # passing a weights= argument. Hence, in both columns: # # printed "Constant" = the coefficient on prec # printed "Se (publication bias)" = the model's reported _cons # # Column 1 reproduces exactly: 0.021 (0.015) p 0.150 and -0.325 (0.262) p 0.220, N = 1,199. # # ------------------------------------------------------------------------------------------ # Column 2, and the one cell this package does NOT reproduce # ------------------------------------------------------------------------------------------ # Column 2 adds country fixed effects. Its "Constant" row reproduces exactly -- 0.021, 0.015, # and p 0.183 to all three printed digits. Its "Se (publication bias)" row is reported as NA, # and the reason is a property of the model rather than a defect in this code. # # 42 countries appear in the estimation sample, but 21 of the 42 country dummies are perfectly # collinear with the study fixed effects: a study that covers exactly one country contributes # no independent country variation. Stata drops 21 of them, one as the xi base category and 20 # more "omitted because of collinearity". The slope on prec, its standard error and every # fitted value are invariant to WHICH 21 are dropped; the split of the fit between _cons and # the surviving country dummies is not. xtreg reports _cons as ybar - xbar'bhat taken over ALL # regressors including those dummies, so in this column the constant is a normalisation of the # dropping order rather than an estimated quantity. # # Measured, not asserted. All three of the following run on the site's own published bma.csv, # all give N = 1,199 and an identical prec coefficient of 0.0206846 with clustered SE # 0.0153147, and all three report a different constant: # # paper, Table 4 col 2 _cons -0.284 (0.305) p 0.357 # authors' own Stata 11 log, 1 Aug 2011 _cons -0.2485 (0.3185) p 0.439 # Stata 15.1 re-run of the same command _cons -0.0649 (0.3099) p 0.835 # # Stata 11 and Stata 15.1 drop different collinear dummies -- Stata 11 omits _Iidcountry_145 # and _155, Stata 15.1 keeps those two and omits _146 and _157 instead -- and so print # different constants for an identical fit. The paper's value matches neither, so it comes # from a still earlier run; the printed -0.284 / 0.305 / 0.357 is already in the earliest # conference-version LaTeX source of this table, and no other Stata log for the paper survives. # There is no honest way to land on it from the published data: reordering the country dummies # moves this constant anywhere in roughly (-0.77, +0.35), so picking an ordering that produced # -0.284 would be choosing it because it matches, not because it is right. Left uncomputed. # # ------------------------------------------------------------------------------------------ # Inference convention for the Table 2 OLS check # ------------------------------------------------------------------------------------------ # Stata's regress y x, vce(cluster g) reports t on G - 1 degrees of freedom, where G is the # number of clusters -- not z. Here G = 41 countries, so df = 40, which is visible in the # authors' log as "F( 16, 40)" and "41 clusters in idcountry". Taking the p-values from # summary()$coeftable applies fixest's default small-sample rule (t.df = "min", i.e. G - 1), # which is Stata's. Reading them instead off st_coefs(), whose default is z, understates them: # 0.072 against the printed 0.080, and 0.069 against 0.077 -- close enough to be mistaken for # rounding, and wrong. if (file.exists("stata_compat.R")) source("stata_compat.R") else source("https://meta-analysis.cz/bma/replication/stata_compat.R") d <- read.csv((if (file.exists("bma.csv")) "bma.csv" else "https://meta-analysis.cz/data/v1/bma/bma.csv"), stringsAsFactors = FALSE) cat("raw rows read:", nrow(d), "\n") ## ---- sample construction (determinants.do lines 14, 26, 123) ---- d <- st_drop_if(d, d$aux == 1) # line 14: drop if aux==1 d <- st_drop_if(d, d$horiz != 1) # line 26: drop if horiz!=1 (keep horizontal spillovers) d <- st_drop_if(d, abs(d$e) > 10) # line 123: drop if abs(e)>10 d$prec <- 1 / d$se # line 17: gen prec = 1/se d$idcountry_f <- factor(d$idcountry) cat("N after sample construction:", nrow(d), "\n\n") ## ---- Table 4, column 1: study fixed effects ---- ## xtreg t prec, fe vce(cluster idstudy) m1 <- st_xtreg_fe(t ~ prec, data = d, panel = "idstudy", cluster = "idstudy") s1 <- summary(m1)$coeftable constant1 <- c(coef = s1["prec", "Estimate"], se = s1["prec", "Std. Error"], p = s1["prec", "Pr(>|t|)"]) cons1_m <- st_xtreg_fe_cons(y = "t", x = "prec", panel = "idstudy", data = d, cluster = ~idstudy) s1c <- summary(cons1_m)$coeftable sepub1 <- c(coef = s1c["(Intercept)", "Estimate"], se = s1c["(Intercept)", "Std. Error"], p = s1c["(Intercept)", "Pr(>|t|)"]) N1 <- nobs(m1) ## ---- Table 4, column 2: study and country fixed effects ---- ## xi: xtreg t prec i.idcountry, fe vce(cluster idstudy) m2 <- st_xtreg_fe(t ~ prec + idcountry_f, data = d, panel = "idstudy", cluster = "idstudy") s2 <- summary(m2)$coeftable constant2 <- c(coef = s2["prec", "Estimate"], se = s2["prec", "Std. Error"], p = s2["prec", "Pr(>|t|)"]) N2 <- nobs(m2) ## How many of the country dummies survive their collinearity with the study fixed effects. ## This count is the whole reason the column-2 constant is not reported: the fit is identical ## for every choice of which dummies are dropped, and the reported constant is not. n_country <- length(unique(d$idcountry)) n_kept <- sum(grepl("^idcountry_f", rownames(s2))) cat(sprintf("Table 4 col 2: %d countries; %d country dummies estimable alongside the study\n", n_country, n_kept)) cat(sprintf(" fixed effects, %d absorbed by them. The constant xtreg prints is a\n", n_country - n_kept)) cat(" normalisation of the dropped set, so it is left uncomputed here.\n") sepub2 <- c(coef = NA_real_, se = NA_real_, p = NA_real_) ## ================================================================================ ## HEADLINE NUMBERS FROM THE PAPER'S OWN TEXT ## ================================================================================ ## meta-analysis.cz summarises this paper as: "spillovers are zero on average but depend ## systematically on the technology gap and ownership structure." That tracks the paper: ## Abstract: "horizontal spillovers are on average zero, but their sign and magnitude ## depend systematically on the characteristics of the domestic economy and foreign ## investors." ## Concluding remarks: "On average, horizontal spillovers are negligible... when the ## technology gap ... is too large, horizontal spillovers are small... investment projects ## in the form of joint ventures with domestic firms bring more positive spillovers than ## fully foreign-owned projects." ## ## (A) "zero on average". Table 1 reports the raw mean of the collected estimates of e as ## -0.002 (std. dev. 0.905). The do-file also computes a fixed-effect and a random-effect ## precision-weighted pooled average, annotated inline with its own printed values: ## metan e se, fixed // 0.017 (determinants.do line 147) ## metan e se, random // -0.011 (determinants.do line 148) ## ## (B) "depend systematically on technology gap and ownership structure". Section 4 reports a ## "Frequentist check (OLS)" column beside the BMA estimates in Table 2: all potential ## spillover determinants plus the control variables with PIP > 0.1, "clustered at the ## country level". That is the do-file's only other estimation line (line 143): ## reg e lngap sim open findev gp95 human fdiint green serv cs aggr bothbf empl ## local lnschcit lnciteaut, vce(cluster idcountry) ## Matching that variable list, in order, to Table 2's printed OLS rows identifies the ## Stata mnemonics: lngap = ln(Technology gap), green = Fully owned, sim = Similarity, ## open/100 = Trade openness, findev/100 = Financial dev., gp95 = Patent rights, ## human/100 = Human capital, fdiint/100 = FDI penetration, serv = Service sectors, ## cs = Cross-sectional, aggr = Aggregated, bothbf = Forward, empl = Employment, ## local = Regional, lnschcit = ln(1+schcit/(2010.6-pubdate)) = Study citations, ## lnciteaut = ln(1+citeaut) = Author citations. The mapping check below confirms it: ## every constructed variable reproduces Table 1's published mean for its named ## counterpart. Table 2 prints, for the two determinants the conclusion singles out: ## Technology gap coef -0.260 se 0.145 p 0.080 ## Fully owned coef -0.104 se 0.057 p 0.077 ## ---- variable construction (determinants.do lines 41/45, 47, 56, 60-61, 65-66) ---- d$lngap <- log(d$gap) # line 56: gen lngap=ln(gap) d$open100 <- d$open / 100 # line 66: replace open=open/100 d$findev100 <- d$findev / 100 # line 65: replace findev=findev/100 d$human100 <- d$human / 100 # line 60: replace human=human/100 d$fdiint100 <- d$fdiint / 100 # line 61: replace fdiint=fdiint/100 d$lnschcit <- log(1 + d$schcit / (2010.6 - d$pubdate)) # lines 41, 45 d$lnciteaut <- log(1 + d$citeaut) # line 47 ## ---- mapping check: constructed variables must reproduce Table 1's published moments ---- map_check <- data.frame( var = c("lngap", "sim", "open100", "findev100", "gp95", "human100", "fdiint100", "green", "serv", "cs", "aggr", "bothbf", "empl", "local"), label = c("Technology gap", "Similarity", "Trade openness", "Financial dev.", "Patent rights", "Human capital", "FDI penetration", "Fully owned", "Service sectors", "Cross-sectional", "Aggregated", "Forward", "Employment", "Regional"), table1_mean = c(9.771, 0.628, 0.709, 0.600, 3.052, 0.269, 0.267, 0.078, 0.062, 0.088, 0.034, 0.704, 0.139, 0.048) ) map_check$produced_mean <- sapply(map_check$var, function(v) mean(d[[v]], na.rm = TRUE)) cat("\n---- variable-mapping check against Table 1 ----\n") print(map_check, digits = 3) ## ---- (A) average effect: raw mean and precision-weighted fixed/random pooling ---- mean_e <- mean(d$e) fe_pool <- st_metan(d$e, d$se, random = FALSE) re_pool <- st_metan(d$e, d$se, random = TRUE) fe_coef <- unname(coef(fe_pool)) re_coef <- unname(coef(re_pool)) ## ---- (B) OLS "frequentist check" of Table 2, clustered at the country level ---- m_freq <- st_regress( e ~ lngap + sim + open100 + findev100 + gp95 + human100 + fdiint100 + green + serv + cs + aggr + bothbf + empl + local + lnschcit + lnciteaut, data = d, cluster = ~idcountry ) ## Stata's regress, vce(cluster g) inference: t on G - 1 df, not z. summary()$coeftable ## carries exactly that (fixest default ssc, t.df = "min"); st_coefs() would report z. fq <- summary(m_freq)$coeftable gap_row <- fq["lngap", ] green_row <- fq["green", ] N_freq <- nobs(m_freq) df_freq <- fixest::degrees_freedom(m_freq, "t") G_freq <- length(unique(d$idcountry[fixest::obs(m_freq)])) cat("\n---- Table 2 frequentist-check coefficients of interest ----\n") print(fq[c("lngap", "green"), ], digits = 6) cat("N used (matches the paper's stated 1,195 of 1,199):", N_freq, "\n") cat("clusters in the estimation sample:", G_freq, " t degrees of freedom used:", df_freq, " (the authors' log prints \"F( 16, 40)\" and \"41 clusters in idcountry\")\n") ## ---- collect and print ---- res <- list( "T4 col1 (study FE) Constant coef" = unname(constant1["coef"]), "T4 col1 (study FE) Constant SE" = unname(constant1["se"]), "T4 col1 (study FE) Constant p" = unname(constant1["p"]), "T4 col1 (study FE) Se(pub.bias) coef" = unname(sepub1["coef"]), "T4 col1 (study FE) Se(pub.bias) SE" = unname(sepub1["se"]), "T4 col1 (study FE) Se(pub.bias) p" = unname(sepub1["p"]), "T4 col1 N" = N1, "T4 col2 (study+country FE) Constant coef" = unname(constant2["coef"]), "T4 col2 (study+country FE) Constant SE" = unname(constant2["se"]), "T4 col2 (study+country FE) Constant p" = unname(constant2["p"]), "T4 col2 (study+country FE) Se(pub.bias) coef" = unname(sepub2["coef"]), "T4 col2 (study+country FE) Se(pub.bias) SE" = unname(sepub2["se"]), "T4 col2 (study+country FE) Se(pub.bias) p" = unname(sepub2["p"]), "T4 col2 N" = N2, "Headline: mean(e), all collected estimates" = mean_e, "Headline: metan e se, fixed (pooled avg.)" = fe_coef, "Headline: metan e se, random (pooled avg.)" = re_coef, "Headline: Table2 OLS check, Technology gap coef" = unname(gap_row["Estimate"]), "Headline: Table2 OLS check, Technology gap SE" = unname(gap_row["Std. Error"]), "Headline: Table2 OLS check, Technology gap p" = unname(gap_row["Pr(>|t|)"]), "Headline: Table2 OLS check, Fully owned coef" = unname(green_row["Estimate"]), "Headline: Table2 OLS check, Fully owned SE" = unname(green_row["Std. Error"]), "Headline: Table2 OLS check, Fully owned p" = unname(green_row["Pr(>|t|)"]), "Headline: Table2 OLS check N" = N_freq ) cat("\n---- produced values ----\n") for (nm in names(res)) cat(sprintf("%-45s %s\n", nm, format(res[[nm]], digits = 6))) cat("\n================================================================================\n") cat("PAPER'S HEADLINE CLAIM: \"spillovers are zero on average but depend systematically\n") cat("on the technology gap and ownership structure.\"\n") cat("================================================================================\n") cat(sprintf(" (A) zero on average:\n")) cat(sprintf(" raw mean of e, N=%d ................. paper (Table 1): -0.002 produced: %8.4f\n", nrow(d), mean_e)) cat(sprintf(" precision-weighted, fixed effect ..... paper (do-file): 0.017 produced: %8.4f\n", fe_coef)) cat(sprintf(" precision-weighted, random effect .... paper (do-file): -0.011 produced: %8.4f\n", re_coef)) cat(sprintf(" (B) depends systematically on technology gap and ownership (Table 2, OLS check, N=%d):\n", N_freq)) cat(sprintf(" Technology gap: coef %.3f (paper -0.260) se %.3f (paper 0.145) p %.3f (paper 0.080)\n", gap_row["Estimate"], gap_row["Std. Error"], gap_row["Pr(>|t|)"])) cat(sprintf(" Fully owned: coef %.3f (paper -0.104) se %.3f (paper 0.057) p %.3f (paper 0.077)\n", green_row["Estimate"], green_row["Std. Error"], green_row["Pr(>|t|)"])) cat("================================================================================\n") stata_compat_log() if (!requireNamespace("jsonlite", quietly = TRUE)) install.packages("jsonlite", repos = "https://cloud.r-project.org") jsonlite::write_json(res, "results.json", auto_unbox = TRUE, na = "null", digits = 10) cat("\nWrote results.json\n")