Different results when lm() is used vs. matrix multiplication formula

Question

I am running a simple multivariate regression on a panel/time-series dataset, using lm() and the underlying formula $(X'X)^{-1} X'Y$

I'm expecting to get the same coefficient values from the two methods. However, I get completely different estimates.

Here is the R code:

  return = matrix(ret.ff.zoo, ncol = 50)  # y vector
  data = cbind(df$EQ, df$EFF, df$SIZE, df$MOM, df$MSCR, df$SY, df$UMP)   # x vector
  
  #First method     
  BETA = solve(crossprod(data)) %*% crossprod(data, return)
  
  #Second method
  OLS <- lm(return ~ data)

I am not sure why the estimates are different between the two methods.

Answer 1

Your example isn't reproducible, but if you try it with some dummy data, the matrix formula and lm produce the same results when you take out the intercept:

set.seed(1)

x <- matrix(rnorm(1000),ncol=5)
y <- rnorm(200)

solve(t(x) %*% x) %*% t(x) %*% y
              [,1]
[1,] -0.0826496646
[2,] -0.0165735273
[3,] -0.0009412659
[4,]  0.0070475728
[5,] -0.0642452777
> lm(y ~ x + 0)

Call:
lm(formula = y ~ x + 0)

Coefficients:
        x1          x2          x3          x4          x5  
-0.0826497  -0.0165735  -0.0009413   0.0070476  -0.0642453