Regressions

Load applicable packages and data

require(tidyverse) #

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require(tidyverse) #
require(janitor) # clean column names

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#require(ivpanel) # iv regressors in panel data
require(ivreg)

Loading required package: ivreg
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require(stargazer) #display our regression results in a nice publishable table

Loading required package: stargazer
Warning: package ‘stargazer’ was built under R version 4.0.5

Please cite as: 

 Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
 R package version 5.2.3. https://CRAN.R-project.org/package=stargazer 

require(plm)

Loading required package: plm
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Attaching package: ‘plm’

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require(lmtest)

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require(janitor) # clean column names
#require(ivpanel) # iv regressors in panel data
require(ivreg)
require(stargazer) #display our regression results in a nice publishable table
require(plm)
require(lmtest)
X1 <- read.csv("X1.csv") %>% 
  clean_names() #piping prevents an umlaut over the i

Regressions

Set 1: OLS and Omitted Instruments and Fixed Effects

Reg01 <- lm(hur~taxcorp + ud + cbc +brr1y + ttr + inf_gdpd
            +pslm + epl +wsc, data=X1)

Reg02 <- ivreg(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
               | ud + cbc + + brr1y + ttr + inf_gdpd, data = X1)
# plm will not work without instruments
#Reg02 <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
#               | ud + cbc + + brr1y + ttr + inf_gdpd, data = X1)

(1): Pooled

FE2SLS_P <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
                |. + ud + cbc +  brr1y + ttr + inf_gdpd +pslm + epl + wsc, 
                data = X1, model = "pooling")

(1a): within

FE2SLS_W <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
                |. + ud + cbc +  brr1y + ttr + inf_gdpd +pslm + epl + wsc, 
                data = X1, model = "within")

(2): Time Effects

FE2SLS_T <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
                + factor(i_time1)
                |. + ud + cbc +  brr1y + ttr + inf_gdpd +pslm + epl + wsc
                + factor(i_time1), 
                data = X1, model = "within", effect = "time")

(2a): Time Effects Experiment

FE2SLS_T1 <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
                + factor(i_time1)
                |. + ud + cbc +  brr1y + ttr + inf_gdpd +pslm + epl + wsc
                + factor(i_time1), 
                data = X1, model = "within")

(3): Locational Effects

FE2SLS_L <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
               + factor(location1)
                 |. + ud + cbc +  brr1y + ttr + inf_gdpd +pslm + epl + wsc
                + factor(location1), 
                data = X1, model = "within", effect="individual")

(4): Time and Locational Effects

FE2SLS_LT <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
                 + factor(location1) + factor(i_time1)
                 |. + ud + cbc +  brr1y + ttr + inf_gdpd +pslm + epl + wsc
                 + factor(location1) + factor(i_time1), 
                 data = X1, model = "within")

(5): Time and locational effects reverse order experiment

• an attempt to figure out why (3) and (4) are exactly the same

FE2SLS_TL <- plm(hur ~ taxcorp + ud + cbc + brr1y + ttr + inf_gdpd 
                + factor(i_time1) + factor(location1)
                  |. + ud + cbc +  brr1y + ttr + inf_gdpd +pslm + epl + wsc
                 + factor(i_time1) + factor(location1), 
                 effect = "twoways", data = X1, model = "within")

Output results

stargazer(Reg01, Reg02, FE2SLS_P, FE2SLS_W, FE2SLS_T, FE2SLS_L,  FE2SLS_TL,
          type = "html", title = "Table 2: Regressions to Explain Unemployment Rate", 
          keep = c("taxcorp", "ud","cbc","brr1y", "ttr","inf_gdpd", "hur", "pslm", "epl","wsc", "Constant"),
          column.labels = c("OLS", "2SLS w/o instruments", "2SLS Pooled", "2SLS Within",
                            "2SLS Time Fixed Effects", "2SLS Individual Fixed Effects", "2SLS Individual and Time Fixed Effects")
          )

<table style="text-align:center"><caption><strong>Table 2: Regressions to Explain Unemployment Rate</strong></caption>
<tr><td colspan="8" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td colspan="7"><em>Dependent variable:</em></td></tr>
<tr><td></td><td colspan="7" style="border-bottom: 1px solid black"></td></tr>
<tr><td style="text-align:left"></td><td colspan="7">hur</td></tr>
<tr><td style="text-align:left"></td><td><em>OLS</em></td><td><em>instrumental</em></td><td colspan="5"><em>panel</em></td></tr>
<tr><td style="text-align:left"></td><td><em></em></td><td><em>variable</em></td><td colspan="5"><em>linear</em></td></tr>
<tr><td style="text-align:left"></td><td>OLS</td><td>2SLS w/o instruments</td><td>2SLS Pooled</td><td>2SLS Within</td><td>2SLS Time Fixed Effects</td><td>2SLS Individual Fixed Effects</td><td>2SLS Individual and Time Fixed Effects</td></tr>
<tr><td style="text-align:left"></td><td>(1)</td><td>(2)</td><td>(3)</td><td>(4)</td><td>(5)</td><td>(6)</td><td>(7)</td></tr>
<tr><td colspan="8" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">taxcorp</td><td>-0.501<sup>***</sup></td><td>-1.008<sup>**</sup></td><td>-0.804<sup>***</sup></td><td>-0.735<sup>***</sup></td><td>-0.326</td><td>-0.326</td><td>-0.326</td></tr>
<tr><td style="text-align:left"></td><td>(0.134)</td><td>(0.424)</td><td>(0.137)</td><td>(0.142)</td><td>(0.199)</td><td>(0.199)</td><td>(0.199)</td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">ud</td><td>-0.004</td><td>-0.019</td><td>-0.023</td><td>-0.032<sup>**</sup></td><td>0.281<sup>***</sup></td><td>0.281<sup>***</sup></td><td>0.281<sup>***</sup></td></tr>
<tr><td style="text-align:left"></td><td>(0.014)</td><td>(0.017)</td><td>(0.014)</td><td>(0.015)</td><td>(0.063)</td><td>(0.063)</td><td>(0.063)</td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">cbc</td><td>0.042<sup>***</sup></td><td>0.051<sup>***</sup></td><td>0.052<sup>***</sup></td><td>0.048<sup>***</sup></td><td>0.131<sup>***</sup></td><td>0.131<sup>***</sup></td><td>0.131<sup>***</sup></td></tr>
<tr><td style="text-align:left"></td><td>(0.011)</td><td>(0.010)</td><td>(0.010)</td><td>(0.010)</td><td>(0.035)</td><td>(0.035)</td><td>(0.035)</td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">brr1y</td><td>-0.006</td><td>0.006</td><td>0.004</td><td>0.005</td><td>0.036<sup>***</sup></td><td>0.036<sup>***</sup></td><td>0.036<sup>***</sup></td></tr>
<tr><td style="text-align:left"></td><td>(0.010)</td><td>(0.010)</td><td>(0.009)</td><td>(0.009)</td><td>(0.011)</td><td>(0.011)</td><td>(0.011)</td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">ttr</td><td>-0.137<sup>***</sup></td><td>-0.145<sup>***</sup></td><td>-0.134<sup>**</sup></td><td>-0.097<sup>*</sup></td><td>-0.062</td><td>-0.062</td><td>-0.062</td></tr>
<tr><td style="text-align:left"></td><td>(0.048)</td><td>(0.054)</td><td>(0.054)</td><td>(0.056)</td><td>(0.088)</td><td>(0.088)</td><td>(0.088)</td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">inf_gdpd</td><td>-0.207<sup>**</sup></td><td></td><td>-0.050</td><td>0.015</td><td>-0.340<sup>***</sup></td><td>-0.340<sup>***</sup></td><td>-0.340<sup>***</sup></td></tr>
<tr><td style="text-align:left"></td><td>(0.102)</td><td></td><td>(0.109)</td><td>(0.118)</td><td>(0.080)</td><td>(0.080)</td><td>(0.080)</td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">pslm</td><td>1.727<sup>***</sup></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td>(0.320)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">epl</td><td>0.543<sup>***</sup></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td>(0.202)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">wsc</td><td>-1.306<sup>***</sup></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td>(0.174)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">Constant</td><td>11.818<sup>***</sup></td><td>12.849<sup>***</sup></td><td>12.085<sup>***</sup></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td>(1.309)</td><td>(2.055)</td><td>(1.435)</td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td colspan="8" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>357</td><td>357</td><td>357</td><td>357</td><td>357</td><td>357</td><td>357</td></tr>
<tr><td style="text-align:left">R<sup>2</sup></td><td>0.367</td><td>0.194</td><td>0.199</td><td>0.180</td><td>0.406</td><td>0.782</td><td>0.263</td></tr>
<tr><td style="text-align:left">Adjusted R<sup>2</sup></td><td>0.350</td><td>0.182</td><td>0.185</td><td>0.121</td><td>0.298</td><td>0.742</td><td>0.128</td></tr>
<tr><td style="text-align:left">Residual Std. Error</td><td>2.881 (df = 347)</td><td>3.233 (df = 351)</td><td></td><td></td><td></td><td></td><td></td></tr>
<tr><td style="text-align:left">F Statistic</td><td>22.338<sup>***</sup> (df = 9; 347)</td><td></td><td>86.870<sup>***</sup></td><td>73.118<sup>***</sup></td><td>205.954<sup>***</sup></td><td>1,081.220<sup>***</sup></td><td>107.421<sup>***</sup></td></tr>
<tr><td colspan="8" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td colspan="7" style="text-align:right"><sup>*</sup>p<0.1; <sup>**</sup>p<0.05; <sup>***</sup>p<0.01</td></tr>
</table>

Tests

F Test: test of individual and/or time effects based on the comparison of the within and pooling model

OLS1 <- lm(hur~taxcorp, data=X1)
pFW <- plm(hur~taxcorp, data=X1, model="within")

pFtest(pFW,OLS1)

    F test for individual effects

data:  hur ~ taxcorp
F = 1.2415, df1 = 18, df2 = 337, p-value = 0.2256
alternative hypothesis: significant effects

“Class Test”

class(X1$location1)

[1] "character"

Coefficient Test

AIC(ct)

numeric(0)