STATA Code:

We first use Hsiang’s STATA code to compute the corrected standard errors (spatHAC in the output below). This routine takes just over 25 seconds.

cd "~/Dropbox/ConleySEs/Data"
clear; use "new_testspatial.dta"

tab year, gen(yy_)
tab FIPS, gen(FIPS_)

timer on 1
ols_spatial_HAC EmpClean00 HDD yy_*FIPS_2-FIPS_362, lat(lat ) lon(lon ) t(year) p(FIPS) dist(500) lag(5) bartlett disp

# *-----------------------------------------------
# *    Variable |   OLS      spatial    spatHAC
# *-------------+---------------------------------
# *         HDD |   -0.669     -0.669     -0.669
# *             |    0.608      0.786      0.838

timer off 1
timer list 1
#  1:     24.8 /        3 =      8.2650

R Code:

Using the same data and options as the STATA code, we then estimate the adjusted standard errors using our new R function. This requires us to first estimate our regression model using the felm function from the lfe package.

# Loading sample data:
dta_file <- "~/Dropbox/ConleySEs/Data/new_testspatial.dta"
DTA <-data.table(read.dta(dta_file))
setnames(DTA, c("latitude", "longitude"), c("lat", "lon"))

# Loading R function to compute Conley SEs:
source("~/Dropbox/ConleySEs/ConleySEs_17June2015.R")

ptm <-proc.time()

# We use the felm() from the lfe package to estimate model with year and county fixed effects.
# Two important points:
# (1) We specify our latitude and longitude coordinates as the cluster variables, so that they are included in the output (m).
# (2) We specify keepCx = TRUE, so that the centered data is included in the output (m).

m <-felm(EmpClean00 ~HDD -1 |year +FIPS |0 |lat +lon,
  data = DTA[!is.na(EmpClean00)], keepCX = TRUE)

coefficients(m) %>%round(3) # Same as the STATA result.
   HDD 
-0.669 

We then feed this model to our function, as well as the cross-sectional unit (county FIPS codes), time unit (year), geo-coordinates (lat and lon), the cutoff for serial correlation (5 years), the cutoff for spatial correlation (500 km), and the number of cores to use.

SE <-ConleySEs(reg = m,
    unit = "FIPS", 
    time = "year",
    lat = "lat", lon = "lon",
    dist_fn = "SH", dist_cutoff = 500, 
    lag_cutoff = 5,
    cores = 1, 
    verbose = FALSE) 

sapply(SE, sqrt) %>%round(3) # Same as the STATA results.
        OLS     Spatial Spatial_HAC 
      0.608       0.786       0.837 
proc.time() -ptm
   user  system elapsed 
  1.619   0.055   1.844 

Estimating the model and computing the standard errors requires just over 1 second, making it over 20 times faster than the comparable STATA routine.

R Using Multiple Cores:

Even with a single core, we realize significant speed improvements. However, the gains are even more dramatic when we employ multiple cores. Using 4 cores, we can cut the estimation of the standard errors down to around 0.4 seconds. (These replications employ the Haversine distance formula, which is more time-consuming to compute.)

pkgs <-c("rbenchmark", "lineprof")
invisible(sapply(pkgs, require, character.only = TRUE))

bmark <-benchmark(replications = 25,
  columns = c('replications','elapsed','relative'),
  ConleySEs(reg = m,
    unit = "FIPS", time = "year", lat = "lat", lon = "lon",
    dist_fn = "Haversine", lag_cutoff = 5, cores = 1, verbose = FALSE),
  ConleySEs(reg = m,
    unit = "FIPS", time = "year", lat = "lat", lon = "lon",
    dist_fn = "Haversine", lag_cutoff = 5, cores = 2, verbose = FALSE),
  ConleySEs(reg = m,
    unit = "FIPS", time = "year", lat = "lat", lon = "lon",
    dist_fn = "Haversine", lag_cutoff = 5, cores = 4, verbose = FALSE))
bmark %>%mutate(avg_eplased = elapsed /replications, cores = c(1, 2, 4))
  replications elapsed relative avg_eplased cores
1           25   23.48    2.095      0.9390     1
2           25   15.62    1.394      0.6249     2
3           25   11.21    1.000      0.4483     4

Given the prevalence of panel data that exhibits both serial and spatial dependence, we hope this function will be a useful tool for applied econometricians working in R.

Feedback Appreciated: Memory vs. Speed Tradeoff

This was Darin’s first foray into C++, so we welcome feedback on how to improve the code. In particular, we would appreciate thoughts on how to overcome a memory vs. speed tradeoff we encountered. (You can email Darin at darinc[at]stanford.edu.)

The most computationally intensive chunk of our code computes the distance from each unit to every other unit. To cut down on the number of distance calculations, we can fill the upper triangle of the distance matrix and then copy it to the lower triangle. With [math]N[/math] units, this requires only  [math](N (N-1) /2)[/math] distance calculations.

However, as the number of units grows, this distance matrix becomes too large to store in memory, especially when executing the code in parallel. (We tried to use a sparse matrix, but this was extremely slow to fill.) To overcome this memory issue, we can avoid constructing a distance matrix altogether. Instead, for each unit, we compute the vector of distances from that unit to every other unit. We then only need to store that vector in memory. While that cuts down on memory use, it requires us to make twice as many   [math](N (N-1))[/math]  distance calculations.

As the number of units grows, we are forced to perform more duplicate distance calculations to avoid memory constraints – an unfortunate tradeoff. (See the functions XeeXhC and XeeXhC_Lg in ConleySE.cpp.)

sessionInfo()
R version 3.2.2 (2015-08-14)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.10.4 (Yosemite)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods  
[7] base     

other attached packages:
 [1] RcppArmadillo_0.5.400.2.0 Rcpp_0.12.0              
 [3] geosphere_1.4-3           sp_1.1-1                 
 [5] lfe_2.3-1709              Matrix_1.2-2             
 [7] ggplot2_1.0.1             foreign_0.8-65           
 [9] data.table_1.9.4          dplyr_0.4.2              
[11] knitr_1.11               

loaded via a namespace (and not attached):
 [1] Formula_1.2-1    magrittr_1.5     MASS_7.3-43     
 [4] munsell_0.4.2    xtable_1.7-4     lattice_0.20-33 
 [7] colorspace_1.2-6 R6_2.1.1         stringr_1.0.0   
[10] plyr_1.8.3       tools_3.2.2      parallel_3.2.2  
[13] grid_3.2.2       gtable_0.1.2     DBI_0.3.1       
[16] htmltools_0.2.6  yaml_2.1.13      assertthat_0.1  
[19] digest_0.6.8     reshape2_1.4.1   formatR_1.2     
[22] evaluate_0.7.2   rmarkdown_0.8    stringi_0.5-5   
[25] compiler_3.2.2   scales_0.2.5     chron_2.3-47    
[28] proto_0.3-10