Problem Set 3
Behavioral Economics, Boston College
Sal Pollastro
# Clear the workspace
rm(list = ls()) # Clear environment
gc() # Clear unused memory## used (Mb) gc trigger (Mb) max used (Mb)
## Ncells 450160 24.1 966700 51.7 638942 34.2
## Vcells 804234 6.2 8388608 64.0 1633131 12.5cat("\f") # Clear the consoleSet-up and background
The assignment is worth 100 points. There are 27 questions. You should have the following packages installed:
library(tidyverse)
library(patchwork)
library(fixest)
library(lmtest)
library(sandwich)In this problem set you will summarize the paper “Do Workers Work More if Wages Are High? Evidence from a Randomized Field Experiment” (Fehr and Goette, AER 2007) and recreate some of its findings.
1 Big picture
[Q1] What is the main question asked in this paper?
The main question of the paper is measuring hours worked and productivity from wage increases. Does increasing wages make people work more and work harder?
[Q2] Recall the taxi cab studies where reference dependence is studied using observational data. What can an experimental study do that an observational study can’t?
Experimental studies allow the researchers to control variables. Observational studies don’t have as much control. In the messenger study, there were things out of the researchers control that might have affected the results such as the type of bike, fitness of the rider, etc.
[Q3] Summarize the field experiment design.
There are two groups of bike messengers. One group spent four weeks working and had a 25% wage increase. The other group spent four weeks working with no wage increase. The key feature of this study is that the wage increase was exogenous and transitory so lifelong income was irrelevant.
[Q4] Summarize the laboratory experiment design. Why was it included with the study?
The laboratory experiment measured individual levels and responses to loss aversion. This was included to explain the negative affect on productivity.
[Q5] Summarize the main results of the field experiment.
The field experiment resulted in a positive impact on labor supply but a negative impact on effort. This means that as wage increases, the messengers will work more hours but the productivity (revenue per shift) decreases.
[Q6] Summarize the main results of the laboratory experiment.
The results of the laboratory experiment were that the level of loss aversion in each messenger drove the negative impact on productivity per shift. Those messengers that had higher levels of loss aversion saw lower productivity.
[Q7] Why are these results valuable? What have we learned? Motivate your discussion with a real-world example.
These results are definitely valuable as they show the affect of wages on productivity. Increasing wages doesn’t necessarily increase productivity per person. An example of this in the real-world could be raising wages on Instacart to incent new shoppers. I shopped for instacart for bit and on the day I would go shop, I tried to maximize my earnings and minimize my costs. Raising the amount a shopper would earn would actually decrease my productivity because if I could earn the amount I typically earn in a day on 3 trips versus 5, then I would actually wouldn’t work as hard. I would want to conserve gas for the next shopping session and I could earn just as much in 3 trips.
2 Replication
Use theme_classic() for all plots.
2.1 Correlations in revenues across firms
For this section please use dailycorrs.csv.
setwd("/Users/spoll/OneDrive/Documents/Boston College/Behavioral Economics/Week 4")
dailycorrs = read.csv("dailycorrs.csv"
, check.names = FALSE
, stringsAsFactors = FALSE
, na.strings = ""
)[Q8] The authors show that earnings at Veloblitz and Flash are correlated. Show this with a scatter plot with a regression line and no confidence interval. Title your axes and the plot appropriately. Do not print the plot but assign it to an object called
p1.
p1 = dailycorrs %>%
ggplot(aes(x = logv, y = logf)) +
geom_point() +
geom_smooth(method = lm
, se = FALSE) +
labs(x = "Veloblitz"
, y = "Flash"
, title = "Earnings") +
theme_classic()[Q9] Next plot the kernel density estimates of revenues for both companies. Overlay the distributions and make the densities transparent so they are easily seen. Title your axes and the plot appropriately. Do not print the plot but assign it to an object called
p2.
p2 = dailycorrs %>%
pivot_longer(c(logf, logv)) %>%
ggplot(aes(x = value, fill = name)) +
geom_density() +
labs(x = "Earnings"
, y = "density"
, title = "Earnings Density")[Q11] Now combine both plots using
library(patchwork)and label the plots with letters.
p1 + p2
2.2 Tables 2 and 3
For this section please use tables1to4.csv.
tables1to4 = read.csv("tables1to4.csv"
, check.names = FALSE
, stringsAsFactors = FALSE
, na.strings = ""
)2.2.1 Table 2
On page 307 the authors write:
“Table 2 controls for individual fixed effects by showing how, on average, the messengers’ revenues deviate from their person-specific mean revenues. Thus, a positive number here indicates a positive deviation from the person-specific mean; a negative number indicates a negative deviation.”
[Q12] Fixed effects are a way to control for heterogeneity across individuals that is time invariant. Why would we want to control for fixed effects? Give a reason how bike messengers could be different from each other, and how these differences might not vary over time.
Fixed effects should controlled in order to avoid avoid differences between messengers skewing the results. These differences could be the type of bike they have, the fitness level of the messenger, age, etc. These differences don’t happen over night and cannot affect the study.
[Q13] Create a variable called
totrev_feand add it to the dataframe. This requires you to “average out” each individual’s revenue for a block from their average revenue: \(x_i^{fe} = x_{it} - \bar{x}_i\) where \(x_i^{fe}\) is the fixed effect revenue for \(i\).
tables1to4 = tables1to4 %>%
group_by(fahrer) %>%
mutate(totrev_fe = totrev - mean(totrev))[Q14] Use
summarise()to recreate the findings in Table 2 for “Participating Messengers” using your new variabletotrev_fe. (You do not have to calculate the differences in means.)In addition to calculating the fixed-effect controled means, calculate the standard errors. Recall the standard error is \(\frac{s_{jt}}{\sqrt{n_{jt}}}\) where \(s_{jt}\) is the standard deviation for treatment \(j\) in block \(t\) and \(n_{jt}\) are the corresponding number of observations.
(Hint: use
n()to count observations.) Each calculation should be named to a new variable. Assign the resulting dataframe to a new dataframe calleddf_avg_revenue.
df_avg_revenue = tables1to4 %>%
drop_na(odd) %>%
group_by(odd, block) %>%
summarise(n = n()
,mean_rev = mean(totrev_fe)
, se_rev = sd(totrev_fe)/sqrt(n))
df_avg_revenue## # A tibble: 6 x 5
## # Groups: odd [2]
## odd block n mean_rev se_rev
## <int> <int> <int> <dbl> <dbl>
## 1 0 1 19 -120. 303.
## 2 0 2 20 -278. 241.
## 3 0 3 20 392. 251.
## 4 1 1 21 -48.9 361.
## 5 1 2 22 722. 193.
## 6 1 3 22 -675. 289.[Q15] Plot
df_avg_revenue. Use points for the means and error bars for standard errors of the means.
To dodge the points and size them appropriately, use
geom_point(position=position_dodge(width=0.5), size=4)To place the error bars use
geom_errorbar(aes(
x=block,
ymin = mean_rev - se_rev, ymax = mean_rev + se_rev),
width = .1,
position=position_dodge(width=0.5))You will need to replace [MEAN] with whatever you named your average revenues and [SE] with whatever you named your standard errors.
p3 = df_avg_revenue %>%
ggplot(aes(x = block
, y = mean_rev
, group = odd
, col = factor(odd))
) +
geom_errorbar(aes(
x=block,
ymin = mean_rev - se_rev, ymax = mean_rev + se_rev),
width = .1,
position=position_dodge(width=0.5)
) +
geom_point(position=position_dodge(width=0.5), size=4) +
labs(x = "Block"
, y = "Avg Revenue"
, title = "Table 2: Participating Messengers"
, fill = "odd") +
theme_classic()
p3
[Q16] Interpret the plot.
The chart above shows the distribution around the mean for each group. The graph shows that after block 1, the variance in average revenue between the groups gets significantly larger.
2.2.2 Table 3
[Q17] Recreate the point estimates in Model (1) in Table 3 by hand (you don’t need to worry about the standard errors). Assign it to object
m1. Recreating this model requires you to control for individual fixed effects and estimate the following equation where \(\text{H}\) is the variablehigh, \(\text{B2}\) is the second block (block == 2) and \(\text{B3}\) is the third block (block == 3):
\[ y_{ijt} - \bar{y}_{ij} = \beta_1 (\text{H}_{ijt} - \bar{\text{H}}_{ij}) + \beta_2 (\text{B2}_{ijt} - \bar{\text{B2}}_{ij}) + \beta_3 (\text{B3}_{ijt} - \bar{\text{B3}}_{ij}) + (\varepsilon_{ijt} - \bar{\varepsilon}_{ij}) \]
tables1to4 = tables1to4 %>%
group_by(fahrer) %>%
mutate(totrev_mean = totrev - mean(totrev)
, high_mean = high - mean(high)
, block2_mean = block2 - mean(block2)
, block3_mean = block3 - mean(block3))
m1 =lm(totrev_mean ~ high_mean + block2_mean + block3_mean, data = tables1to4)
m1##
## Call:
## lm(formula = totrev_mean ~ high_mean + block2_mean + block3_mean,
## data = tables1to4)
##
## Coefficients:
## (Intercept) high_mean block2_mean block3_mean
## 7.575e-14 1.076e+03 -2.900e+02 -6.759e+02[Q18] Now recreate the same point estimates using
lmand assign it to objectm2. You are estimating the model below where where \(\text{F}_i\) is the dummy variable for each messenger (fahrer). Make sure to cluster the standard errors at the messenger level. (Uselmtestandsandwhichfor this.)
\[ y_{ijt} - \beta_0 + \beta_1 \text{H}_{ijt} + \beta_2 \text{B2}_{ijt} + \beta_3 \text{B3}_{ijt} + \sum_{i=1}^{n} \alpha_i \text{F}_i + \varepsilon_{ijt} \]
m2 = lm(totrev ~ high + block2 + block3 + factor(fahrer), data = tables1to4)
m2##
## Call:
## lm(formula = totrev ~ high + block2 + block3 + factor(fahrer),
## data = tables1to4)
##
## Coefficients:
## (Intercept) high block2 block3
## 1657.531 1076.175 -289.964 -675.904
## factor(fahrer)2 factor(fahrer)3 factor(fahrer)4 factor(fahrer)5
## 436.700 747.200 -666.408 -1247.485
## factor(fahrer)6 factor(fahrer)7 factor(fahrer)8 factor(fahrer)9
## 1537.500 750.167 -106.967 3912.200
## factor(fahrer)10 factor(fahrer)11 factor(fahrer)12 factor(fahrer)13
## -817.742 2936.092 -1228.575 -965.908
## factor(fahrer)14 factor(fahrer)15 factor(fahrer)16 factor(fahrer)17
## 884.000 -39.967 191.725 -469.908
## factor(fahrer)18 factor(fahrer)19 factor(fahrer)20 factor(fahrer)21
## 1327.367 2658.967 -726.275 -514.133
## factor(fahrer)22 factor(fahrer)23 factor(fahrer)24 factor(fahrer)25
## 2955.600 3330.233 1759.167 61.167
## factor(fahrer)26 factor(fahrer)27 factor(fahrer)28 factor(fahrer)29
## -265.742 -579.275 -150.167 -1048.242
## factor(fahrer)30 factor(fahrer)31 factor(fahrer)32 factor(fahrer)33
## 1557.533 -737.967 -526.100 2173.200
## factor(fahrer)34 factor(fahrer)35 factor(fahrer)36 factor(fahrer)37
## 9107.033 -64.000 2054.900 2193.967
## factor(fahrer)38 factor(fahrer)39 factor(fahrer)40 factor(fahrer)41
## 1836.933 225.892 -175.575 -902.075
## factor(fahrer)42 factor(fahrer)43 factor(fahrer)44 factor(fahrer)45
## 3938.033 -1070.575 521.867 569.767
## factor(fahrer)46 factor(fahrer)47 factor(fahrer)48 factor(fahrer)49
## 153.958 -781.242 -524.775 1044.200
## factor(fahrer)50 factor(fahrer)51 factor(fahrer)52 factor(fahrer)53
## 6590.667 5288.967 4278.300 3433.033
## factor(fahrer)54 factor(fahrer)55 factor(fahrer)56 factor(fahrer)57
## -143.908 976.267 1761.800 2471.533
## factor(fahrer)58 factor(fahrer)59 factor(fahrer)60 factor(fahrer)61
## 1353.200 -117.108 931.033 664.700
## factor(fahrer)62 factor(fahrer)63 factor(fahrer)64 factor(fahrer)65
## 33.258 -238.185 2372.873 -268.627
## factor(fahrer)66 factor(fahrer)67 factor(fahrer)68 factor(fahrer)69
## 490.373 -387.242 2408.092 -343.908
## factor(fahrer)70 factor(fahrer)71 factor(fahrer)72 factor(fahrer)73
## -336.575 -1030.908 -1151.908 -346.575
## factor(fahrer)74 factor(fahrer)75 factor(fahrer)76 factor(fahrer)77
## -626.242 2799.425 1052.092 -703.908
## factor(fahrer)78 factor(fahrer)79 factor(fahrer)80 factor(fahrer)81
## -364.242 -1258.242 -257.908 -980.575
## factor(fahrer)82 factor(fahrer)83 factor(fahrer)84 factor(fahrer)85
## -1277.575 470.425 -622.908 -888.242
## factor(fahrer)86 factor(fahrer)87 factor(fahrer)88 factor(fahrer)89
## 989.092 17.758 -1170.242 -1171.242
## factor(fahrer)90 factor(fahrer)91 factor(fahrer)92 factor(fahrer)93
## 629.425 -3.908 -33.242 4841.758
## factor(fahrer)94 factor(fahrer)95 factor(fahrer)96 factor(fahrer)97
## 15.425 -424.575 275.373 -814.242
## factor(fahrer)98 factor(fahrer)99 factor(fahrer)100 factor(fahrer)101
## 581.092 -1272.575 2382.425 -1193.575
## factor(fahrer)102 factor(fahrer)103 factor(fahrer)104 factor(fahrer)105
## 384.758 1992.758 1431.758 -979.575
## factor(fahrer)106 factor(fahrer)107 factor(fahrer)108 factor(fahrer)109
## -749.908 -804.242 1573.092 -48.908
## factor(fahrer)110 factor(fahrer)111 factor(fahrer)112 factor(fahrer)113
## 1386.425 -1247.908 -88.908 -767.908
## factor(fahrer)114 factor(fahrer)115 factor(fahrer)116 factor(fahrer)117
## -1045.908 410.092 -634.575 248.758
## factor(fahrer)118 factor(fahrer)119 factor(fahrer)120 factor(fahrer)121
## -1300.908 68.425 -58.242 1257.425
## factor(fahrer)122 factor(fahrer)123 factor(fahrer)124 factor(fahrer)125
## 1016.092 1699.903 -434.597 -841.097
## factor(fahrer)126 factor(fahrer)127 factor(fahrer)128 factor(fahrer)129
## -977.242 -1082.242 -151.242 455.092
## factor(fahrer)130 factor(fahrer)131 factor(fahrer)132 factor(fahrer)133
## -352.597 -725.097 -156.597 259.373
## factor(fahrer)134 factor(fahrer)135 factor(fahrer)136 factor(fahrer)137
## 122.373 -396.627 -855.627 396.373
## factor(fahrer)138
## -483.627m2_clustered = coeftest(m2, vcov. = vcovCL, cluster = ~fahrer)
m2_clustered##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.6575e+03 1.5283e+02 1.0846e+01 < 2.2e-16 ***
## high 1.0762e+03 2.9055e+02 3.7039e+00 0.0002624 ***
## block2 -2.8996e+02 2.0063e+02 -1.4453e+00 0.1496600
## block3 -6.7590e+02 2.3798e+02 -2.8402e+00 0.0048873 **
## factor(fahrer)2 4.3670e+02 1.5181e-10 2.8767e+12 < 2.2e-16 ***
## factor(fahrer)3 7.4720e+02 1.5159e-10 4.9290e+12 < 2.2e-16 ***
## factor(fahrer)4 -6.6641e+02 9.6851e+01 -6.8807e+00 4.946e-11 ***
## factor(fahrer)5 -1.2475e+03 7.6413e+01 -1.6326e+01 < 2.2e-16 ***
## factor(fahrer)6 1.5375e+03 1.5145e-10 1.0152e+13 < 2.2e-16 ***
## factor(fahrer)7 7.5017e+02 1.5137e-10 4.9558e+12 < 2.2e-16 ***
## factor(fahrer)8 -1.0697e+02 1.5157e-10 -7.0572e+11 < 2.2e-16 ***
## factor(fahrer)9 3.9122e+03 1.5150e-10 2.5822e+13 < 2.2e-16 ***
## factor(fahrer)10 -8.1774e+02 9.6851e+01 -8.4433e+00 2.737e-15 ***
## factor(fahrer)11 2.9361e+03 9.6851e+01 3.0315e+01 < 2.2e-16 ***
## factor(fahrer)12 -1.2286e+03 9.6851e+01 -1.2685e+01 < 2.2e-16 ***
## factor(fahrer)13 -9.6591e+02 9.6851e+01 -9.9731e+00 < 2.2e-16 ***
## factor(fahrer)14 8.8400e+02 1.5170e-10 5.8272e+12 < 2.2e-16 ***
## factor(fahrer)15 -3.9967e+01 1.5186e-10 -2.6319e+11 < 2.2e-16 ***
## factor(fahrer)16 1.9173e+02 9.6851e+01 1.9796e+00 0.0488701 *
## factor(fahrer)17 -4.6991e+02 9.6851e+01 -4.8518e+00 2.178e-06 ***
## factor(fahrer)18 1.3274e+03 1.5209e-10 8.7272e+12 < 2.2e-16 ***
## factor(fahrer)19 2.6590e+03 1.5109e-10 1.7598e+13 < 2.2e-16 ***
## factor(fahrer)20 -7.2627e+02 9.6851e+01 -7.4989e+00 1.178e-12 ***
## factor(fahrer)21 -5.1413e+02 1.5149e-10 -3.3938e+12 < 2.2e-16 ***
## factor(fahrer)22 2.9556e+03 1.5129e-10 1.9536e+13 < 2.2e-16 ***
## factor(fahrer)23 3.3302e+03 1.5177e-10 2.1943e+13 < 2.2e-16 ***
## factor(fahrer)24 1.7592e+03 1.5210e-10 1.1566e+13 < 2.2e-16 ***
## factor(fahrer)25 6.1167e+01 1.5137e-10 4.0407e+11 < 2.2e-16 ***
## factor(fahrer)26 -2.6574e+02 9.6851e+01 -2.7438e+00 0.0065222 **
## factor(fahrer)27 -5.7927e+02 9.6851e+01 -5.9811e+00 7.803e-09 ***
## factor(fahrer)28 -1.5017e+02 1.5149e-10 -9.9127e+11 < 2.2e-16 ***
## factor(fahrer)29 -1.0482e+03 9.6851e+01 -1.0823e+01 < 2.2e-16 ***
## factor(fahrer)30 1.5575e+03 1.5154e-10 1.0278e+13 < 2.2e-16 ***
## factor(fahrer)31 -7.3797e+02 1.5157e-10 -4.8687e+12 < 2.2e-16 ***
## factor(fahrer)32 -5.2610e+02 1.5170e-10 -3.4679e+12 < 2.2e-16 ***
## factor(fahrer)33 2.1732e+03 1.5146e-10 1.4348e+13 < 2.2e-16 ***
## factor(fahrer)34 9.1070e+03 1.5161e-10 6.0067e+13 < 2.2e-16 ***
## factor(fahrer)35 -6.4000e+01 1.5155e-10 -4.2231e+11 < 2.2e-16 ***
## factor(fahrer)36 2.0549e+03 1.5159e-10 1.3555e+13 < 2.2e-16 ***
## factor(fahrer)37 2.1940e+03 1.5138e-10 1.4493e+13 < 2.2e-16 ***
## factor(fahrer)38 1.8369e+03 1.5147e-10 1.2127e+13 < 2.2e-16 ***
## factor(fahrer)39 2.2589e+02 9.6851e+01 2.3324e+00 0.0204929 *
## factor(fahrer)40 -1.7557e+02 9.6851e+01 -1.8128e+00 0.0710821 .
## factor(fahrer)41 -9.0207e+02 9.6851e+01 -9.3140e+00 < 2.2e-16 ***
## factor(fahrer)42 3.9380e+03 1.5147e-10 2.5998e+13 < 2.2e-16 ***
## factor(fahrer)43 -1.0706e+03 9.6851e+01 -1.1054e+01 < 2.2e-16 ***
## factor(fahrer)44 5.2187e+02 1.5161e-10 3.4422e+12 < 2.2e-16 ***
## factor(fahrer)45 5.6977e+02 1.5140e-10 3.7634e+12 < 2.2e-16 ***
## factor(fahrer)46 1.5396e+02 9.6851e+01 1.5896e+00 0.1132067
## factor(fahrer)47 -7.8124e+02 9.6851e+01 -8.0664e+00 3.230e-14 ***
## factor(fahrer)48 -5.2477e+02 9.6851e+01 -5.4184e+00 1.437e-07 ***
## factor(fahrer)49 1.0442e+03 1.5168e-10 6.8841e+12 < 2.2e-16 ***
## factor(fahrer)50 6.5907e+03 1.5130e-10 4.3560e+13 < 2.2e-16 ***
## factor(fahrer)51 5.2890e+03 1.5127e-10 3.4963e+13 < 2.2e-16 ***
## factor(fahrer)52 4.2783e+03 1.5181e-10 2.8182e+13 < 2.2e-16 ***
## factor(fahrer)53 3.4330e+03 1.5296e-10 2.2444e+13 < 2.2e-16 ***
## factor(fahrer)54 -1.4391e+02 9.6851e+01 -1.4859e+00 0.1385999
## factor(fahrer)55 9.7627e+02 1.5202e-10 6.4222e+12 < 2.2e-16 ***
## factor(fahrer)56 1.7618e+03 1.5141e-10 1.1636e+13 < 2.2e-16 ***
## factor(fahrer)57 2.4715e+03 1.5150e-10 1.6313e+13 < 2.2e-16 ***
## factor(fahrer)58 1.3532e+03 1.5132e-10 8.9427e+12 < 2.2e-16 ***
## factor(fahrer)59 -1.1711e+02 9.6851e+01 -1.2092e+00 0.2277690
## factor(fahrer)60 9.3103e+02 1.5163e-10 6.1401e+12 < 2.2e-16 ***
## factor(fahrer)61 6.6470e+02 1.5128e-10 4.3938e+12 < 2.2e-16 ***
## factor(fahrer)62 3.3258e+01 9.6851e+01 3.4340e-01 0.7315953
## factor(fahrer)63 -2.3818e+02 7.6413e+01 -3.1171e+00 0.0020447 **
## factor(fahrer)64 2.3729e+03 1.5961e+02 1.4867e+01 < 2.2e-16 ***
## factor(fahrer)65 -2.6863e+02 1.5961e+02 -1.6830e+00 0.0936498 .
## factor(fahrer)66 4.9037e+02 1.5961e+02 3.0723e+00 0.0023643 **
## factor(fahrer)67 -3.8724e+02 9.6851e+01 -3.9983e+00 8.449e-05 ***
## factor(fahrer)68 2.4081e+03 9.6851e+01 2.4864e+01 < 2.2e-16 ***
## factor(fahrer)69 -3.4391e+02 9.6851e+01 -3.5509e+00 0.0004603 ***
## factor(fahrer)70 -3.3657e+02 9.6851e+01 -3.4752e+00 0.0006037 ***
## factor(fahrer)71 -1.0309e+03 9.6851e+01 -1.0644e+01 < 2.2e-16 ***
## factor(fahrer)72 -1.1519e+03 9.6851e+01 -1.1894e+01 < 2.2e-16 ***
## factor(fahrer)73 -3.4657e+02 9.6851e+01 -3.5784e+00 0.0004166 ***
## factor(fahrer)74 -6.2624e+02 9.6851e+01 -6.4660e+00 5.408e-10 ***
## factor(fahrer)75 2.7994e+03 9.6851e+01 2.8904e+01 < 2.2e-16 ***
## factor(fahrer)76 1.0521e+03 9.6851e+01 1.0863e+01 < 2.2e-16 ***
## factor(fahrer)77 -7.0391e+02 9.6851e+01 -7.2679e+00 4.872e-12 ***
## factor(fahrer)78 -3.6424e+02 9.6851e+01 -3.7608e+00 0.0002119 ***
## factor(fahrer)79 -1.2582e+03 9.6851e+01 -1.2992e+01 < 2.2e-16 ***
## factor(fahrer)80 -2.5791e+02 9.6851e+01 -2.6629e+00 0.0082597 **
## factor(fahrer)81 -9.8057e+02 9.6851e+01 -1.0124e+01 < 2.2e-16 ***
## factor(fahrer)82 -1.2776e+03 9.6851e+01 -1.3191e+01 < 2.2e-16 ***
## factor(fahrer)83 4.7043e+02 9.6851e+01 4.8572e+00 2.125e-06 ***
## factor(fahrer)84 -6.2291e+02 9.6851e+01 -6.4316e+00 6.566e-10 ***
## factor(fahrer)85 -8.8824e+02 9.6851e+01 -9.1712e+00 < 2.2e-16 ***
## factor(fahrer)86 9.8909e+02 9.6851e+01 1.0213e+01 < 2.2e-16 ***
## factor(fahrer)87 1.7758e+01 9.6851e+01 1.8340e-01 0.8546698
## factor(fahrer)88 -1.1702e+03 9.6851e+01 -1.2083e+01 < 2.2e-16 ***
## factor(fahrer)89 -1.1712e+03 9.6851e+01 -1.2093e+01 < 2.2e-16 ***
## factor(fahrer)90 6.2943e+02 9.6851e+01 6.4989e+00 4.490e-10 ***
## factor(fahrer)91 -3.9083e+00 9.6851e+01 -4.0400e-02 0.9678440
## factor(fahrer)92 -3.3242e+01 9.6851e+01 -3.4320e-01 0.7317249
## factor(fahrer)93 4.8418e+03 9.6851e+01 4.9992e+01 < 2.2e-16 ***
## factor(fahrer)94 1.5425e+01 9.6851e+01 1.5930e-01 0.8735915
## factor(fahrer)95 -4.2457e+02 9.6851e+01 -4.3838e+00 1.732e-05 ***
## factor(fahrer)96 2.7537e+02 1.5961e+02 1.7253e+00 0.0857414 .
## factor(fahrer)97 -8.1424e+02 9.6851e+01 -8.4071e+00 3.476e-15 ***
## factor(fahrer)98 5.8109e+02 9.6851e+01 5.9998e+00 7.057e-09 ***
## factor(fahrer)99 -1.2726e+03 9.6851e+01 -1.3139e+01 < 2.2e-16 ***
## factor(fahrer)100 2.3824e+03 9.6851e+01 2.4599e+01 < 2.2e-16 ***
## factor(fahrer)101 -1.1936e+03 9.6851e+01 -1.2324e+01 < 2.2e-16 ***
## factor(fahrer)102 3.8476e+02 9.6851e+01 3.9727e+00 9.350e-05 ***
## factor(fahrer)103 1.9928e+03 9.6851e+01 2.0575e+01 < 2.2e-16 ***
## factor(fahrer)104 1.4318e+03 9.6851e+01 1.4783e+01 < 2.2e-16 ***
## factor(fahrer)105 -9.7957e+02 9.6851e+01 -1.0114e+01 < 2.2e-16 ***
## factor(fahrer)106 -7.4991e+02 9.6851e+01 -7.7429e+00 2.557e-13 ***
## factor(fahrer)107 -8.0424e+02 9.6851e+01 -8.3039e+00 6.866e-15 ***
## factor(fahrer)108 1.5731e+03 9.6851e+01 1.6242e+01 < 2.2e-16 ***
## factor(fahrer)109 -4.8908e+01 9.6851e+01 -5.0500e-01 0.6140247
## factor(fahrer)110 1.3864e+03 9.6851e+01 1.4315e+01 < 2.2e-16 ***
## factor(fahrer)111 -1.2479e+03 9.6851e+01 -1.2885e+01 < 2.2e-16 ***
## factor(fahrer)112 -8.8908e+01 9.6851e+01 -9.1800e-01 0.3595285
## factor(fahrer)113 -7.6791e+02 9.6851e+01 -7.9287e+00 7.835e-14 ***
## factor(fahrer)114 -1.0459e+03 9.6851e+01 -1.0799e+01 < 2.2e-16 ***
## factor(fahrer)115 4.1009e+02 9.6851e+01 4.2342e+00 3.246e-05 ***
## factor(fahrer)116 -6.3457e+02 9.6851e+01 -6.5520e+00 3.319e-10 ***
## factor(fahrer)117 2.4876e+02 9.6851e+01 2.5685e+00 0.0108089 *
## factor(fahrer)118 -1.3009e+03 9.6851e+01 -1.3432e+01 < 2.2e-16 ***
## factor(fahrer)119 6.8425e+01 9.6851e+01 7.0650e-01 0.4805517
## factor(fahrer)120 -5.8242e+01 9.6851e+01 -6.0140e-01 0.5481625
## factor(fahrer)121 1.2574e+03 9.6851e+01 1.2983e+01 < 2.2e-16 ***
## factor(fahrer)122 1.0161e+03 9.6851e+01 1.0491e+01 < 2.2e-16 ***
## factor(fahrer)123 1.6999e+03 1.2521e+02 1.3577e+01 < 2.2e-16 ***
## factor(fahrer)124 -4.3460e+02 1.2521e+02 -3.4710e+00 0.0006126 ***
## factor(fahrer)125 -8.4110e+02 1.2521e+02 -6.7177e+00 1.281e-10 ***
## factor(fahrer)126 -9.7724e+02 9.6851e+01 -1.0090e+01 < 2.2e-16 ***
## factor(fahrer)127 -1.0822e+03 9.6851e+01 -1.1174e+01 < 2.2e-16 ***
## factor(fahrer)128 -1.5124e+02 9.6851e+01 -1.5616e+00 0.1196766
## factor(fahrer)129 4.5509e+02 9.6851e+01 4.6989e+00 4.365e-06 ***
## factor(fahrer)130 -3.5260e+02 1.2521e+02 -2.8161e+00 0.0052564 **
## factor(fahrer)131 -7.2510e+02 1.2521e+02 -5.7912e+00 2.133e-08 ***
## factor(fahrer)132 -1.5660e+02 1.2521e+02 -1.2507e+00 0.2122334
## factor(fahrer)133 2.5937e+02 1.5961e+02 1.6250e+00 0.1054443
## factor(fahrer)134 1.2237e+02 1.5961e+02 7.6670e-01 0.4440046
## factor(fahrer)135 -3.9663e+02 1.5961e+02 -2.4849e+00 0.0136259 *
## factor(fahrer)136 -8.5563e+02 1.5961e+02 -5.3607e+00 1.914e-07 ***
## factor(fahrer)137 3.9637e+02 1.5961e+02 2.4833e+00 0.0136853 *
## factor(fahrer)138 -4.8363e+02 1.5961e+02 -3.0300e+00 0.0027075 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1[Q20] Now use
feolsto recreate Model (1), including the standard errors. Assign your estimates to the objectm3. You are estimating the model below where where \(\alpha_i\) is the individual intercept (i.e. the individual fixed effect):
\[ y_{ijt} = \alpha_i + \beta_1 \text{H}_{ijt} + \beta_2 \text{B2}_{ijt} + \beta_3 \text{B3}_{ijt} + \varepsilon_{ijt} \]
m3 = feols(totrev_mean ~ high_mean + block2_mean + block3_mean, data = tables1to4)
m3## OLS estimation, Dep. Var.: totrev_mean
## Observations: 386
## Standard-errors: IID
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.510000e-14 53.1225 2.840000e-16 1.0000e+00
## high_mean 1.076175e+03 206.9707 5.199649e+00 3.2612e-07 ***
## block2_mean -2.899636e+02 138.4748 -2.093981e+00 3.6920e-02 *
## block3_mean -6.759039e+02 137.6668 -4.909707e+00 1.3541e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 1,038.3 Adj. R2: 0.094831[Q21] Compare the estimates in
m1,m2andm3. What is the same? What is different? What would you say is the main advantage of usingfelm()?
The coefficient estimates in all models were the same, yet the standard errors were different.
[Q22] Explain why you need to cluster the standard errors.
Clustering the standard errors helps to eliminate any autocorrelation between the messengers of each group.