Does labor negatively affect output (from empirical perspective)? I am estimating Cobb-Douglas production function for US using time series framework:
$$Y_t=A_t \times L_t^\alpha K_t^\beta $$
where $Y$ is output, $A$ is $TFP$, $L$ is labor and $K$ is capital. After log-transformation I estimate the following linear model:
$$lnY_t=\alpha_0+\alpha_1lnL+\alpha_2lnK+\epsilon_t$$
The estimation results are: $\alpha_0=16.8$, $\alpha_1=-0.72$ and $\alpha_2=0.64$. I am concerned about negative coefficient of labor. Is there any theoretical/empirical explanation for it?
The negative coefficient could imply decreasing returns to scale under some specifications. For example, Miller &amp; Upadhyay (2002) show that under certain assumptions (see the paper for details) the Cobb-Douglass functions of a form $Y =AK^{\alpha}L^{\beta}$ could be rewritten as:
$Y =AK^{\alpha}L^{\alpha +\beta-1}\implies \ln Y = \ln A + \alpha \ln K + (\alpha+\beta-1)\ln L$
The authors even find some negative estimates for coefficient on labor, although most of them not statistically significant. However, the study above is done on a panel with short $T$ and might not necessarily be applicable to time series setting that you seem to imply you are having by only including $t$ subscripts.
Moreover, if you just directly applied the specification you are showing above most likely your coefficients are biased so that could be an explanation for this result.
As pointed out by @Bertrand in his +1 comment there is likely to be an endogeneity present, and hence it is common to use methods that address that. For example, the Wooldridge method that relies on GMM is becoming very popular in the literature (see . Wooldridge, 2009), and some older but still popular approaches include the
Levinsohn and Petrin (2003) or Olley and Pakes (1996)  approaches. Also,  Van Beveren, I. (2012). Total factor productivity estimation: A practical review and sources cited therein provide good overview of different estimation methods.
Furthermore, if you are estimating the production function on datasets with long $T$ you need to take into account possible unit-roots (or use some cointegration models) and in addition to the stochastic trends also deterministic ones. If you run this on a time series data I would find it very likely that the result is just due to some stochastic or deterministic trend that was not properly taken into account.